LIST OF CITATIONS of publications by Goulnara N. ARZHANTSEVA

more then 220 citations in total, excluding self-citations and citations of the paper with A. Yu. Ol'shanskii (PhD supervisor).

Last update: Aug. 26, 2011

Papers already published or accepted: 

Summary and comments to my list of publications

[1] G.N. Arzhantseva and E. Guentner, Coarse non-amenability and covers with small eigenvalues,
Mathematische Annalen (2011), to appear.    pdf    NEW !

[2] G.N. Arzhantseva, M. Bridson, T. Januszkiewicz, I. Leary, A. Minasyan, J. Swiatkowski,
Infinite groups with fixed point properties, Geometry & Topology, 13 (2009), 1229-1263.    pdf
11 citations by

M. Bridson, On the dimension of CAT(0) spaces where mapping class groups act, (2009), arXiv.org:0908.0690

M. Bridson, K. Vogtmann, Actions of automorphism groups of free groups on homology spheres and acyclic manifolds, (2008), arXiv.org:0803.2062

I. Chatterji, M. Kassabov, New examples of finitely presented groups with strong fixed point properties, (2008), arXiv.org:0809.3719, to appear in Journal of Topology and Analysis.

D. Fisher, L. Silberman, Groups not acting on manifolds, Int. Math. Res. Not. 16 (2008), 11 pp.

G. Gandini, Cohomological invariants and the classifying space for proper actions, (2011), arXiv.org:1106.3022

T. Januszkiewicz, P.H. Kropholler, I.J. Leary, Groups possessing extensive hierarchical decompositions, (2009), arXiv.org:0908.3669

A. Naor, L. Silberman, Poincaré inequalities, embeddings, and wild groups, (2010), arXiv.org:1005.4084

D. Osajda, A construction of hyperbolic Coxeter groups, (2010), arXiv.org: 1003.0774

D. Osajda, P. Przytycki, Boundaries of systolic groups, Geom. Topol. 13 (2009), no. 5, 2807-2880.

D. Osin, Small cancellations over relatively hyperbolic groups and embedding theorems, Annals of Mathematics, 172 (2010), 1-39.

Sh. Weinberger, Some remarks inspired by the C0 Zimmer program, (2009), preprint.

 

[3] G.N. Arzhantseva, C. Drutu, and M. Sapir, Compression functions of uniform embeddings of groups into
Hilbert and Banach spaces, Journal für die Reine und Angewandte Mathematik, [Crelle's Journal], 633 (2009), 213-235.     pdf
11 citations by

C. Anantharaman-Delaroche, Amenability and exactness for groups, group actions and operator algebras, (2007)

http://www.univ-orleans.fr/mapmo/membres/anantharaman/publications/ESI07.pdf

T. Austin, A. Naor, Y. Peres, The wreath product of  Z with Z has Hilbert compression exponent 2/3, Proc. Amer. Math. Soc. 137 (2009), no. 1, 85-90.

T. Austin, A finitely-generated amenable group with very poor compression into Lebesgue spaces, (2009), arXiv.org:0909.2047

J.-C. Birget, One-way permutations, computational asymmetry and distortion, J. Algebra 320 (2008), no. 11, 4030-4062.

A. Dranishnikov, M. Sapir, On the dimension growth of groups, (2010), arXiv:1008.3868

D. Dreesen, Hilbert space compression for free products and HNN-extension, (2010), arXiv:1002.3879

S. Gal, Asymptotic dimension and uniform embeddings, Groups Geom. Dyn. 2 (2008), no. 1, 63-84. MR2367208 (2009d:20105)

A. Naor, Y. Peres, Embeddings of discrete groups and the speed of random walks, Int. Math. Res. Not. IMRN (2008), Art. ID rnn 076, 34 pp.

A. Naor, Y. Peres, Lp compression, traveling salesmen, and stable walks, arXiv.org:0904.4728

P. Nowak, G. Yu, Large-scale geometry, (2010), EMS publishing house, to appear, http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf

M. Sapir, Some group theory problems, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 1189-1214.

 

[4] G.N. Arzhantseva, V.S. Guba, M. Lustig and J.-Ph. Préaux, Testing Cayley graph densities,
Annales mathematiques Blaise Pascal, 15(2) (2008), 169-221.    abs   pdf
1 citation by

J. Cannon, Amenability, Folner sets, and Cooling Functions, (2009).

 

[5] G.N. Arzhantseva, A. Minasyan and D. Osin, The SQ-universality and residual properties of
relatively hyperbolic groups, Journal of Algebra, 315(1)  (2007), 165-177.    pdf
18 citations by

I. Belegradek, Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements, (2007), arXiv.org:0711.2324

I. Belegradek, D. Osin, Rips construction and Kazhdan property (T), Groups Geom. Dyn. 2 (2008), no. 1, 1-12. MR2367206 (2009c:20076)

I. Belegradek, A. Szczepanski, Endomorphisms of relatively hyperbolic groups, with an appendix by Oleg V. Belegradek. Internat. J. Algebra Comput. 18 (2008), no. 1, 97-110. MR2394723 (2009a:20069) 

D. Bisch, R. Nicoara, S. Popa, Continuous families of hyperfinite subfactors with the same standard invariant, Internat. J. Math. 18 (2007), no.3, 255-267. 

J. O. Button, Large groups of deficiency 1, Israel J. Math. 167 (2008), 111-140. MR2448020 (2009k:20068)

P.-E. Caprace, N. Monod, Isometry groups of non-positively curved spaces: discrete subgroups, J. Topology 2 (2009), no. 4, 701-746. MR2574741

M. Edjvet, A. Vdovina, On the SQ-universality of groups with special presentations, J. Group Theory (2010), 1433-5883.

D. Fisher, L. Silberman, Groups not acting on manifolds, Int. Math. Res. Not. IMRN 2008, no. 16, Art. ID rnn060, 11 pp. MR2435750 (2009f:57059)

Le Thi Giang, The relative hyperbolicity of one-relator relative presentations, J. Group Theory 12 (2009), no. 6, 949-959. MR2582060

T. Januszkiewicz, P. Kropholler, I. Leary, Groups possessing extensive hierarchical decompositions, (2009), arXiv.org:0908.3669

Ant. A. Klyachko, SQ-universality of one-relator relative presentations, Sb. Math. 197 (2006), no. 9-10, 1489-1508. MR2310117 (2008a:20040)

E. Martinez-Pedroza, On quasiconvexity and relative hyperbolic structures, (2008), arXiv.org:0811.2384

A. Minasyan, Groups with finitely many conjugacy classes and their automorphisms, Comment. Math. Helv. 84 (2009), no. 2, 259-296. MR2495795

A. Minasyan, D. Osin, Normal automorphisms of relatively hyperbolic groups, Trans. Amer. Math. Soc. 362 (2010), no. 11, 6079-6103. MR2661509

A. Ol'shanskii, D. Osin, M. Sapir, Lacunary hyperbolic groups, Geom. Topol. 13 (2009), no. 4, 2051-2140. MR2507115

D. Osin, Small cancellations over relatively hyperbolic groups and embedding theorems, Annals of Mathematics, 172 (2010), 1-39.

D. Osin, On the universal theory of torsion and lacunary hyperbolic groups, (2009), arXiv.org:0903.3978

D. Witte Morris, Introduction to arithmetic groups, (2008), arXiv:math/0106063

 

[6] G. N. Arzhantseva and Z.Sunic, Construction of elements in the closure of Grigorchuk group, Geometriae Dedicata, 124(1)  (2007), 17-26.    pdf
2 citations by

B. Demir, M. Saltan, On p-adic integers and the adding machine group, (2010), arXiv:1007.0366

O. Siegenthaler, Discrete and Profinite Groups Acting on Regular Rooted Trees, PhD thesis, Georg-August-Universität Göttingen, 2009,

http://webdoc.sub.gwdg.de/diss/2010/siegenthaler/siegenthaler.pdf

 

[7]  G.N. Arzhantseva, A. Minasyan, Relatively hyperbolic groups are C*-simple,
Journal of Functional Analysis, 243(1)  (2007), 345-351.    pdf
3 citations by

P. de la Harpe, On simplicity of reduced C*-algebras of groups, Bull. Lond. Math. Soc. 39 (2007), no. 1, 1-26. MR2303514 (2008a:22004)

E. Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009), no. 2, 317-342. MR2486802

E. Martinez-Pedroza, On quasiconvexity and relative hyperbolic structures, (2008), arXiv.org:0811.2384

 

[8] G.N. Arzhantseva, P. de la Harpe, D. Kahrobaei, The true prosoluble completion of a group:
Examples and open problems, Geometriae Dedicata, 124(1)  (2007), 5-17.    abs   pdf.
4 citations by

K. Bencsath, A. Douglas, D. Kahrobaei, Some Residually Solvable One-Relator Groups, Irish Math. Soc. Bulletin 65 (2010), 23-31.

S. Friedl, S.Vidussi, Twisted Alexander polynomials and fibered 3-manifolds, 2010, arXiv:1001.0132

D. Kahrobaei, Doubles of residually solvable groups in B. Fine, G. Rosenberger, D. Spellman (eds), Aspects of Infinite Group Theory, Algebra and Discrete Mathematics, World Scientific, 1 (2008), 192-200.

O. Siegenthaler, Discrete and Profinite Groups Acting on Regular Rooted Trees, PhD thesis, Georg-August-Universität Göttingen, 2009,

http://webdoc.sub.gwdg.de/diss/2010/siegenthaler/siegenthaler.pdf

 

[9] G.N. Arzhantseva, V.S. Guba, M.V. Sapir, Metrics on diagram groups and uniform embeddings in a Hilbert space
Commentarii Mathematici Helvetici, 81(4) (2006), 911-929.   abs  pdf.  
24 citations by

C. Anantharaman-Delaroche, Amenability and exactness for groups, group actions and operator algebras,(2007)

http://www.univ-orleans.fr/mapmo/membres/anantharaman/publications/ESI07.pdf

T. Austin, A. Naor, Y. Peres, The wreath product of Z with Z has Hilbert compression exponent 2/3, Proc. Amer. Math. Soc. 137 (2009), no. 1, 85-90.

T. Austin, A finitely-generated amenable group with very poor compression into Lebesgue spaces, (2009), arxiv.org:0909.2047

J.-C. Birget, One-way permutations, computational asymmetry and distortion, J. Algebra 320 (2008), no. 11, 4030-4062.

N. Brodskiy, D. Sonkin, Compression of uniform embeddings into Hilbert space, Topology Appl. 155 (2008), no. 7, 725-732. MR2395586 (2009b:20078)

S. J. Campbell, Property A and affine buildings, J. Funct. Anal. 256 (2009), no. 2, 409-431.

Y. de Cornulier, Y. Stalder, A. Valette, Proper actions of wreath products and generalizations, (2009), arxiv.org:0905.3960

A. Dranishnikov, M. Sapir, On the dimension growth of groups, (2010), arxiv:1008.3868

D. Dreesen, Hilbert space compression under direct limits and certain group extensions (2010), arxiv.org:1009.2014

S. Gal, Asymptotic dimension and uniform embeddings, Groups Geom. Dyn. 2 (2008), no. 1, 63-84.

V. Guba, M.Sapir,  Diagram groups and directed 2-complexes: homotopy and homology, J. Pure Appl. Algebra 205 (2006), no. 1, 1-47. MR2193190 2006j:20056

V. Guba, M. Sapir, On the conjugacy growth functions of groups, (2010), arXiv:1003.1293v2

U. Haagerup, G. Picioroaga, New Presentations of Thompson's group and applications, preprint (14 pp., 2008), arXiv:0812.0037, to appear in J. of Operator Theory.

S. Li, Compression bounds for wreath products, Proc. Amer. Math. Soc. 138 (2010), no. 8, 2701-2714. MR2644886

A. Naor, Y. Peres, Lp compression, traveling salesmen, and stable walks, (2009), arXiv:0904.4728

A. Naor, Y. Peres, Embeddings of discrete groups and the speed of random walks, Int. Math. Res. Not. IMRN 2008, Art. ID rnn 076, 34 pp.

P. Nowak, On exactness and isoperimetric profiles of discrete groups, J. Funct. Anal. 243 (2007), no. 1, 323-344. MR2291440 (2008c:20081)

P. Nowak, G. Yu, Large-Scale geometry, (2010), EMS publishing house, to appear, http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf

S. Passidis, A. Weston, Manifestations of non linear roundness in analysis, discrete geometry and topology, in Limits of graphs in group theory and computer science by G. Arzhantseva, A.Valette (eds.), EPFL press, 2009.

M. Sapir, Some group theory problems, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 1189-1214.

Y. Stalder, A. Valette, Wreath products with the integers, proper actions and Hilbert space compression, Geom. Dedicata 124 (2007), 199-211.

R. Tessera, Quantitative property A, Poincaré inequalities, Lp-compression and Lp-distortion for metric measure spaces, Geom. Dedicata 136 (2008), 203-220.  MR2443353

R. Tessera, Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces, (2006), arXiv.org:math/0603138

G. Yu, Higher index theory of elliptic operators and geometry of groups. International Congress of Mathematicians. Vol. II, 1623-1639, Eur. Math. Soc., Zürich, 2006. 

 

[10] G.N. Arzhantseva, A dichotomy for finitely generated subgroups of word hyperbolic groups,
  Contemporary Mathematics, 394, Amer. Math.Soc., Providence, RI, 2006, 1-11.    abs  intro  ps   
5 citations by

M. Gromov, Singularities, expanders and topology of maps. I. Homology versus volume in the spaces of cycles. Geom. Funct. Anal. 19 (2009), no. 3, 743-841. MR2563769

I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236

I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)

I. Kapovich, R. Weidmann, Nielsen methods and groups acting on hyperbolic spaces, Geom. Dedicata 98 (2003), 95-121. MR1988426 (2004e:20076)

H. Reza Rostami, About groups with property (U), Armenian journal of mathematics, 3(1) (2008), 14-22.


[11] G.N. Arzhantseva and I.G. Lysenok, A lower bound on the growth of word hyperbolic groups, 
 Journal of the London Mathematical Society, (2) 73 (2006), 109-125.    abs   pdf
2 citations by

J. Button, Non proper HNN extensions and uniform uniform exponential growth, (2009), arXiv.org:0909.2841

F. Zuddas, Some finiteness results for groups with bounded algebraic entropy, Geom. Dedicata (2009), 49-62.

 

[12] G.N. Arzhantseva, V.S. Guba, L.Guyot, Growth rates of amenable groups,
Journal of Group Theory, 8 (2005), no.3, 389-394.
   abs   ps
1 citation by

V. Guba, Strict dead-end elements in free soluble groups, Comm. Algebra 36 (2008), no. 5, 1988-1997. MR2424281 (2009d:20074)

  

[13] G.N. Arzhantseva, J. Burillo, M. Lustig, L. Reeves, H. Short, E. Ventura, Uniform non-amenability,
 Advances in Mathematics, 197 (2005), no. 2, 499-522.    abs  intro  pdf
18 citations by

J. Anderson, J. Aramayona, K.J. ShackletonUniformly exponential growth and mapping class groups of surfaces, In the tradition of Ahlfors-Bers. IV, 1-6, 

Contemp. Math., 432, Amer. Math. Soc., Providence, RI, 2007.  

V. Atabekyan, Uniform nonamenability of subgroups of free Burnside groups of odd period, Math. Notes, 85 (4) (2009), 496-502.

J. Bannon, M. Ravichandran, A Følner invariant for type II1 factors, Expo. Math. 25 (2007), no. 2, 117-130. MR2319573 (2008c:46090)

E. Breuillard, T. Gelander, Uniform independence in linear groups, Invent. Math. 173 (2008), no. 2, 225-263. MR2415307 (2009j:20068)

E. Breuillard, T. Gelander, Cheeger constant and algebraic entropy of linear groups, Int. Math. Res. Not. (2005), no. 56, 3511-3523.  MR2200587 (2006m:20061)

J. Burillo, Grups paradoxa de Banach Tarski, Butlletí de la Societat Catalana de Matemàtiques,Vol. 23, núm. 2, 2008. Pàg. 181-199. 

Y. de Cornulier, L. Guyot, W. Pitsch, On the isolated points in the space of groups, J. Algebra 307 (2007), no. 1, 254-277. MR2278053 (2008c:20082)

Y. de Cornulier, L. Guyot. W. PitschThe space of subgroups of an abelian group, (2008), arXiv.org:0811.1549

M. Ershov, A. Jaikin-ZapirainKazhdan quotients of Golod-Shafarevich groups, (2009), arXiv:org:0908.3734

L. Guyot, Y. Stalder, Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups, 2010, arXiv:1001.5371

R. Lyons, M. Pichot, S. Vassout, Uniform non-amenability, cost, and the first l2-Betti number, Groups Geom. Dyn. 2 (2008), no. 4, 595-617. MR2442947 (2009i:20080)

P. Nowak, Isoperimetry of group actions, Adv. Math. 219 (2008), no. 1, 1-26. MR2435418 (2009g:20097)

A.Yu. Olshanskii, M.V. Sapir, On k-free-like groups, Algebra and Logic 48 (2)  (2009), 245-257.

D. Osin, Uniform non-amenability of free Burnside groups, Arch. Math. (Basel) 88 (2007), no. 5, 403-412. MR2316885 (2008e:20067) 

D. OsinL2-Betti numbers and non-unitarizable groups without free subgroups, Int. Math. Res. Not. IMRN2009, no. 22, 4220-4231. MR2552302 (2010k:22007)

M. PichotSemi-continuity of the first l2-Betti number on the space of finitely generated groups, Comment. Math. Helv. 81 (2006), no. 3, 643-652. MR2250857 (2007e:20089)

Y. Stalder, Convergence of Baumslag-Solitar groups, Bull. Belg. Math. Soc. Simon Stevin 13 (2006), no. 2, 221-233. MR2259902 (2008f:20047)

R. Willett, Property A and graphs with large girth, (2011), preprint.

 
[14] G.N. Arzhantseva and P.-A. Cherix, On the Cayley graph of a generic finitely presented group,
 Bulletin of the Belgian Mathematical Society, 11 (2004), no. 4, 589-601.
   abs  intro  ps  
4 citations by

T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint, Journal of Mathematical Sciences, 156 (1) (2009), 56-108.

I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp. 

Y. Ollivier,  Sharp phase transition theorems for hyperbolicity,  Geom. Funct. Anal. 14 (2004), no. 3, 595—679. MR2100673 (2005m:20101)

  

[15] G.N. Arzhantseva and I.G. Lysenok, Growth tightness for word hyperbolic groups,
  Mathematische Zeitschrift, 241 (2002), no. 3, 597--611.   abs  intro  pdf  
14 citations by

L. Bartholdi, R. Grigorchuk, V. Nekrashevych, From fractal groups to fractal sets, Fractals in Graz 2001, 25-118,
Trends Math., Birkhäuser, Basel, 2003. MR2091700 (2005h:20056)

T. Ceccherini-Silberstein, F. Scarabotti, Random walks, entropy and hopfianity of free groups, Random walks and geometry, 413-419, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. MR2087792 (2005h:60131)

T. Ceccherini-Silberstein, W. WoessGrowth and ergodicity of context-free languages, Trans. Amer. Math. Soc. 354 (2002), no. 11, 4597-4625. MR1926891 (2003g:68067)

F. Dal’bo, M. Peigné, J.-C. Picaud, A. Sambusetti, On the growth of quotients of Kleinian groups, Ergod. Th. & Dynam. Sys. (2010), published online.

A. Erschler, Growth rates of small cancellation groups, Random walks and geometry, 421-430, Walter de Gruyter GmbH & Co. KG, Berlin, 2004. MR2087793 (2005f:20061)

P. de la HarpeUniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17. MR1950882 (2003k:20031)

P. de la HarpeTopics in geometric group theory, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000. vi+310 pp. MR1786869 (2001i:20081)

W. Huss, E. Sava, W. Woess, Entropy sensitivity of languages defined by infinite automata, via Markov chains with forbidden transitions, Theoretical Computer Science, 2010, to appear, arXiv:0911.0142

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp. 

Y. OllivierGrowth exponent of generic groups, Comment. Math. Helv. 81 (2006), no. 3, 569-593. MR2250854 (2007d:20120)

A. SambusettiAsymptotic properties of coverings in negative curvature, Geom. Topol. 12 (2008), no. 1, 617-637. MR90354 (2009g:53058)

A. SambusettiGrowth tightness of negatively curved manifolds, C. R. Math. Acad. Sci. Paris 336 (2003), no. 6, 487-491. MR1975085 (2004a:53048)

A. SambusettiGrowth tightness of surface groups, Expo. Math. 20 (2002), no. 4, 345-363. MR1940012 (2003k:57004)

A. Talambutsa,  Attainability of the index of exponential growth in free products of cyclic groups, Math. Notes 78 (2005), no. 3-4, 569-572. MR2226734 (2007a:20028) 

 

[16] G.N. Arzhantseva and D.V. Osin, Solvable groups with polynomial Dehn functions,
 Transactions of the American Mathematical Society, 354 (2002), 3329-3348.    abs  intro  pdf  
9 citations by

D. Kahrobaei, M. Anshel, Decision and Search in Non-Abelian Cramer-Shoup Public Key Cryptosystem, Groups Complex. Cryptol. 1, (2009) no. 2, 217-225. 

N. Broaddus, B. Farb, A. Putman, Irreducible Sp-representations and subgroup distortion in the mapping class group, (2007), arXiv.org:0707.2262

Y. de Cornulier, R. Tessera, Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups, (2010), arXiv:1003.0148 

C. DrutuFilling in solvable groups and in lattices in semisimple groups, Topology 43 (2004), no. 5, 983-1033. MR2079992 (2005h:20078) 

P. Davidson, Geometric methods in the study of Pride groups and relative presentations,  (2008), PhD thesis, University of Glasgow. http://theses.gla.ac.uk/230/01/2008davidsonphd.pdf

W. Dison, T.R. Riley,  Hydra groups, (2010),  arXiv:1002.1945

R. Ji, C. Ogle, B. Ramsey, B-Bounded cohomology and applications,   arXiv:1004.4677 

M. Kassabov, T. Riley, The Dehn function of Baumslag's metabelian group (2010), arXiv:1008.1966

E. Leuzinger, Ch. PittetOn quadratic Dehn functions, Math. Z. 248 (2004), no. 4, 725-755. MR2103539 (2005j:20050)

[17] G.N. Arzhantseva, On quasiconvex subgroups of word hyperbolic groups,
 Geometriae Dedicata, 87 (2001), 191-208.    abs  intro  pdf 
13 citations by  

T. Delzant, M. Gromov, Cuts in Kähler groups, Infinite groups: geometric, combinatorial and dynamical aspects, 31-55, 

Progr. Math., 248, Birkhäuser, Basel, 2005. MR2195452 (2006j:32023)

B. Farb, L. Mosher, Convex cocompact subgroups of mapping class groups, Geom. Topol. 6 (2002), 91-152 (electronic). MR1914566 (2003i:20069)

Y. Glasner, J. Souto, P. Storm, Normal complements to hyperbolic subgroup, (2009), preprint.

P. de la HarpeTopics in geometric group theory, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000. vi+310 pp. MR1786869 (2001i:20081)

E. Jabara, Groups that are the union of a finite number of double cosets, Rend. Sem. Mat. Univ. Padova 116 (2006), 41-53. MR2287342 (2008c:20056)

I. Kapovich, R. Weidmann, Kleinian groups and the rank problem, Geom. Topol. 9 (2005), 375-402. MR2140986 (2006d:20079)

I. KapovichThe Frattini subgroups of subgroups of hyperbolic groups, J. Group Theory 6 (2003), no. 1, 115-126. MR1953799 (2003j:20075)

I. KapovichThe non-amenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups, Enseign. Math. (2) 48 (2002), no. 3-4, 359-375. MR1955607 (2003j:20074)

I. KapovichThe geometry of relative Cayley graphs for subgroups of hyperbolic groups, (2002), arXiv:math/0201045

E. Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups, Groups Geom. Dyn. 3 (2009), no. 2, 317-342. MR2486802

A. MinasyanSome properties of subsets of hyperbolic groups, Comm. Algebra 33 (2005), no. 3, 909-935. MR2128420 (2006c:20088)

A. MinasyanOn products of quasiconvex subgroups in hyperbolic groups, Internat. J. Algebra Comput. 14 (2004), no. 2, 173-195. MR2058319 (2005a:20063)

A. Minasyan, On quasiconvex subsets of hyperbolic groups, (2005), PhD thesis, Vanderbilt University.

[18] G.N. Arzhantseva, A property of subgroups of infinite index in a free group,   Proceedings of the American Mathematical Society, 128 (11) (2000),  3205-3210.   abs  intro  pdf  
19 citations by  

F. Bassino, A. Martino, C. Nicaud, E. Ventura, P. Weil, Statistical properties of subgroups of free groups, (2010), arXiv:1001.4472v1 

A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Generic complexity of the conjugacy problem in HNN-extensions and algorithmic stratification of Miller's groups, Internat. J. Algebra Comput. 17 (2007), no. 5-6, 963-997. MR2355678 (2008m:20046)

A.V. Borovik, A.G. Myasnikov, V.N. Remeslennikov, Multiplicative measures on free groups, Internat. J. Algebra Comput. 13 (2003), no. 6, 705-731. MR2028100 (2004k:20051)

A. Borovik, A.G. Myasnikov, V. Shpilrain, Measuring sets in infinite groups, Computational and statistical group theory (Las Vegas, NV/Hoboken, NJ, 2001), 21-42, Contemp. Math., 298, Amer. Math. Soc., Providence, RI, 2002. MR1929714 (2003m:20024)

L. Ciobanu, A. Martino, E. Ventura, The generic Hanna Neumann Conjecture and Post correspondence problem, (2008), preprint.

J. Friedman, The Strengthened Hanna Neumann Conjecture I: A Combinatorial Proof, (2010), arXiv:1003.5739v3 

V. Kaimanovich, I. Kapovich, P. Schupp, The subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)

I. Kapovich, A. Miasnikov, P. Schupp, V. ShpilrainAverage-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)

I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)

I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236

I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)

I. Kapovich, P. Schupp, V. ShpilrainGeneric properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)

I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)

I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)

I. Kapovich, P. SchuppBounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)

S. Margolis, J. Meakin, Z. Sunik, Distortion functions and the membership problem for submonoids of groups and monoids, Geometric methods in group theory, 109-129, Contemp. Math., 372, Amer. Math. Soc., Providence, RI, 2005. MR2139682 (2005m:20141)

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.  

M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325

B. Solie, Genericity of filling elements, (2010), arXiv:1007.4022

[19] G.N. Arzhantseva, Generic properties of finitely presented groups and Howson's Theorem,
 Communications in Algebra, 26 (11) (1998), 3783-3792.
    mathscinet  intro  
24 citations by 

I. BumaginOn small cancellation k-generated groups with (k-1)-generated subgroups all free, Internat. J. Algebra Comput. 11 (2001), no. 5, 507-524. MR1869228 (2003a:20052)

T. G. Ceccherini-Silberstein, A. Y. Samet-Vaillant, Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint, Journal of Mathematical Sciences, 156 (1) (2009), 56-108.

B. Fine, A. Myasnikov, G. Rosenberger, Generic subgroups of group amalgams, Groups Complex. Cryptol. 1 (2009), no. 1, 51-61. MR2502936

E. Frenkel, A.G. Myasnikov, V.N. RemeslennikovRegular sets and counting in free groups, (2009), arXiv:0906.2850 

R. Gilman, A. Miasnikov, D. Osin, Exponentially generic subsets of groups, (2010), arXiv:1007.0552v1 

E. GhysRandom groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)

P. de la HarpeTopics in geometric group theory, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2000. vi+310 pp. MR1786869 (2001i:20081)

V. Kaimanovich, I. Kapovich, P. SchuppThe subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)

I. Kapovich, A. Miasnikov, P. Schupp, V. ShpilrainAverage-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)

I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)

I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.

I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)

I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)

I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)

I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236

I. Kapovich, P. SchuppBounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)

I. Kapovich, P. Schupp, V. ShpilrainGeneric properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)

I. Kapovich, R. WeidmannFreely indecomposable groups acting on hyperbolic spaces, Internat. J. Algebra Comput. 14 (2004), no. 2, 115-171. MR2058318 (2005f:20079)

M. Lustig, Y. Moria, Horizontal Dehn surgery and genericity in the curve complex, (2007), arXiv:0711.4492v4

Y. OllivierSharp phase transition theorems for hyperbolicity,  Geom. Funct. Anal. 14 (2004), no. 3, 595-679. MR2100673 (2005m:20101)

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp. 

Y. OllivierCritical densities for random quotients of hyperbolic groups, C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 391-394.

M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325.
B. Solie, Genericity of filling elements, (2010), arXiv:1007.4022

[20] G.N.Arzhantseva, On groups in which subgroups with a fixed number of generators are free,
 Fundamental and Applied Mathematics,  3(3) (1997), 675-683 (in Russian).     abs  
18 citations by

Yu. Bahturin, A. Olshanskii, Actions of maximal growth, Proc. London Math. Soc. (2010) 101(1): 27-72

I. BumaginOn small cancellation k-generated groups with (k-1)-generated subgroups all free, Internat. J. Algebra Comput. 11 (2001), no. 5, 507-524. MR1869228 (2003a:20052)

S. Cleary, M. Elder, A. Rechnitzer, J. TabackRandom subgroups of Thompson's group F, (2007), arXiv:0711.1343

E. Frenkel, A.G. Myasnikov, V.N. RemeslennikovRegular sets and counting in free groups, (2009), arXiv:0906.2850

R. Gilman, A. Miasnikov, D. Osin, Exponentially generic subsets of groups, (2010), arXiv:1007.0552v1

E. GhysRandom groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)

V. Kaimanovich, I. Kapovich, P. SchuppThe subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099

I. Kapovich, A. Miasnikov, P. Schupp, V. ShpilrainAverage-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)

I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)

I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.

I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236

I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)

I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)

I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)

I. Kapovich, P. SchuppBounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)

I. Kapovich, P. Schupp, V. ShpilrainGeneric properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068) 

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.

M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325. 

 

[21] G.N. Arzhantseva and A.Yu. Ol'shanskii, Generality of the class of groups in which subgroups
with a lesser number of generators are free,  Mathematical Notes, 59(3-4) (1996), 350-355.    mathscinet  pdf  
28 citations by

I. BumaginOn small cancellation k-generated groups with (k-1)-generated subgroups all free, Internat. J. Algebra Comput. 11 (2001), no. 5, 507-524. MR1869228 (2003a:20052)

S. Cleary, M. Elder, A. Rechnitzer, J. TabackRandom subgroups of Thompson's group F, (2007), arXiv:0711.1343

E. Frenkel, A.G. Myasnikov, V.N. RemeslennikovRegular sets and counting in free groups, (2009), arXiv:0906.2850

E. GhysRandom groups (following Misha Gromov, ...), Astérisque No. 294 (2004), viii, 173-204. MR2111644 (2005j:20049)

L. Guyot, Estimating Minkowski dimensions in the space of marked groups, Ann. Fac. Sci. Toulouse Math. (6) 16 (2007), no. 1, 107-124. MR2325594 (2008e:20063)

P. de la HarpeUniform growth in groups of exponential growth, Geom. Dedicata 95 (2002), 1-17. MR1950882 (2003k:20031)

V. Kaimanovich, I. Kapovich, P. SchuppThe subadditive ergodic theorem and generic stretching factors for free group automorphisms, Israel J. Math. 157 (2007), 1-46. MR2342439 (2009d:20099)

I. Kapovich, A. Miasnikov, P. Schupp, V. ShpilrainAverage-case complexity and decision problems in group theory, Adv. Math. 190 (2005), no. 2, 343-359. MR2102661 (2005i:20053)

I. Kapovich, A. Miasnikov, P. Schupp, V. Shpilrain, Generic-case complexity, decision problems in group theory, and random walks, J. Algebra 264 (2003), no. 2, 665-694. MR1981427 (2005m:20080)

I. Kapovich, I. Rivin, P. Schupp, V. Shpilrain, Densities in free groups and Zk, visible points and test elements, Math. Res. Lett. 14 (2007), no. 2, 263-284.

I. Kapovich, P. Schupp, Random quotients of the modular group are rigid and essentially incompressible, J. Reine Angew. Math. 628 (2009), 91-119. MR2503236

I. Kapovich, P. Schupp, On group-theoretic models of randomness and genericity, Groups Geom. Dyn. 2 (2008), no. 3, 383-404. MR2415305 (2009k:20102)

I. Kapovich, P. Schupp, Delzant's T-invariant, Kolmogorov complexity and one-relator groups, Comment. Math. Helv. 80 (2005), no. 4, 911-933. MR2182705 (2007d:20062)

I. Kapovich, P. Schupp, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups, Math. Ann. 331 (2005), no. 1, 1-19. MR2107437 (2005h:20079)

I. Kapovich, P. SchuppBounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion, Proc. London Math. Soc. (3) 88 (2004), no. 1, 89-113. MR2018959 (2005a:20061)

I. Kapovich, P. Schupp, V. ShpilrainGeneric properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups, Pacific J. Math. 223 (2006), no. 1, 113-140. MR2221020 (2007e:20068)

I. Kapovich, R. Weidmann, Kleinian groups and the rank problem, Geom. Topol. 9 (2005), 375-402. MR2140986 (2006d:20079)

I. Kapovich, R. WeidmannFreely indecomposable groups acting on hyperbolic spaces, Internat. J. Algebra Comput. 14 (2004), no. 2, 115-171. MR2058318 (2005f:20079)

I. Kozakov, Percolation and Ising model on graphs with tree-like structure, (2008), PhD thesis, Vanderbilt University.

S. Margolis, J. Meakin, Z. Sunik, Distortion functions and the membership problem for submonoids of groups and monoids, Geometric methods in group theory, 109-129, Contemp. Math., 372, Amer. Math. Soc., Providence, RI, 2005. MR2139682 (2005m:20141)

L. Markus-Epstein, Stallings foldings and subgroups of amalgams of finite groups, Internat. J. Algebra Comput. 17 (2007), no. 8, 1493-1535. MR2378049 (2009c:20044)

A. Myasnikov, V. Shpilrain, A. Ushakov, Group-based cryptographyBirkhäuser, 2008.

Y. OllivierSharp phase transition theorems for hyperbolicity,  Geom. Funct. Anal. 14 (2004), no. 3, 595-679. MR2100673 (2005m:20101)

Y. OllivierCritical densities for random quotients of hyperbolic groups, C. R. Math. Acad. Sci. Paris 336 (2003), no. 5, 391-394.

Y. Ollivier, A January 2005 invitation to random groups, Ensaios Matemáticos, 10. Sociedade Brasileira de Matemática, Rio de Janeiro, 2005. ii+100 pp.

M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325.

P. Schupp, Coxeter groups, 2-completion, perimeter reduction and subgroup separability, Geom. Dedicata 96 (2003), 179-198. MR1956839 (2003m:20052)

D.T. Wise, Sectional curvature, compact cores, and local quasiconvexity, Geom. Funct. Anal. 14 (2004), no. 2, 433-468. MR2062762 (2005i:53043) 

 

[22] G.N. Arzhantseva, Generic properties of finitely presented groups,
PhD thesis, Moscow Lomonosov State University, December 1998.

Books (edited):

[23]  G.N. Arzhantseva, A.Valette (eds.), Limits of graphs in group theory and computer science,
Fundamental Sciences, EPFL Press, Lausanne, 2009, 305 pp.    book

[24] G.N. Arzhantseva, L. Bartholdi, J. Burillo, and E. Ventura (eds.), Geometric group theory,
Trends in Mathematics, Birkhäuser Verlag, Basel,  2007, 253 pp.   book

Submitted papers and preprints:

[25] G.N. Arzhantseva, J.-F. Lafont, A. Minasyan, Isomorphism versus commensuarability for a class of finitely presented groups,
(2011).   pdf    NEW !

[26] G.N. Arzhantseva, E. Guentner, J. Spakula, Coarse non-amenability and coarse embeddings,
(2011), submitted.   pdf    NEW !
2 citations by

R. Willett, Property A and graphs with large girth, (2011), preprint.

M. Ostrovskii, Low-distortion embeddings of graphs with large girth, (2011), arxiv.org:1108.2542


[27]  G.N. Arzhantseva and T. Delzant, Examples of random groups, Journal of Topology (2008), submitted:
first version (October 28, 2008), revised version (August 26, 2011).     pdf  
16 citations by 

A. Bartels, W. Luck, The Borel conjecture for hyperbolic and CAT(0)-groups, (2009), arXiv.org:0901.0442

Y. de Cornulier, Y. Stalder, A. Valette, Proper actions of wreath products and generalizations, (2009), arxiv.org:0905.3960

R. Coulon, Asphericity and small cancellation theory for rotation family of groups, (2009), arxiv:0907.4577 

R. Coulon, Automorphismes extérieurs du groupe de Burnside libre, PhD thesis, University of Strasbourg, 2010.

E. Guentner, R. Tessera, G. Yu, A notion of geometric complexity and its application to topological rigidity, arxiv:1008.0884v1
V. Lafforgue, Conjecture de Baum-Connes, théorie de Fonataine en caractéristique p, et programme de Langlands géométriques, (2009), Habilitation thesis, University of Paris 7.

W. Lueck, Survey on aspherical manifolds, (2009), arXiv:0902.2480v3

W. Lueck, K- and L-theory of group rings, (2010), arXiv:1003.5002v1

A. Naor, L. Silberman, Poincaré inequalities, embeddings, and wild groups,(2010), arXiv:1005.4084

P. Nowak, G. Yu, Large-Scale geometry, (2010), EMS publishing house, to appear. http://www.math.tamu.edu/~pnowak/book_etb/book_etb.pdf

M. Sapir, Asymptotic invariants, complexity of groups and related problems, (2010), arXiv:1012.1325
M. Sapir, 
Aspherical groups and manifolds with extreme properties, (2011), arXiv:1103.3873
J. Spakula, R. Willett, On rigidity of Roe algebras, (2011), preprint.

R. Willett, Property A and graphs with large girth, (2011), preprint. 
R. Willett, G. Yu, Higher index theory for certain expanders and Gromov monster groups I, (2011), arXiv:1012.4150
R. Willett, G. Yu, Higher index theory for certain expanders and Gromov monster groups II, (2011), arXiv:1012.4151

[28] G.N. Arzhantseva,  An algorithm detecting Dehn presentations,
 preprint, University of Geneva, 2000.   abs  intro  ps  
1 citation by

V. Diekert, A. Duncan, A. Myasnikov, Geodesic rewriting systems and pregroups, (2009), arXiv.org:0906.2223

 

 Papers in Theoretical Computer Science/Applied mathematics (refereed):

[29] G.N. Arzhantseva, J. Díaz, J. Petit, J.D.P. Rolim, and M. Serna, Broadcasting on networks of sensors 
communicating through directional antennas,  Ambient Intelligence Computing,
1-12, Proceedings, CTI Press and Ellinika Grammata, 2003.    abs  ps 

[30] G.N. Arzhantseva and J.D.P. Rolim, Considerations for a geometric model of the web,
 Approximation and Randomization Algorithms in Communication Networks, Rome, 2002,
1-11, Proceedings, Carleton Scientific.    abs

[31] G.N. Arzhantseva and J.D.P. Rolim, Computability and Complexity,   e-learning theoretical 
course of the Virtual Logic Laboratory (a project of the Swiss Virtual Campus), 90 pp. (electronic tutorial).    abs

Papers in preparation:

G.N. Arzhantseva and M. Lustig, A first course in geometric group theory, graduate textbook project.
G.N. Arzhantseva, Geometry of small cancellation and Burnside factors, lecture notes of the Borel seminar minicourse.
G. N. Arzhantseva, Infinite groups: Growth and Isoperimetry, lecture notes, the IIIe Cycle Romand de mathématiques.

Conference announcements:

G.N. Arzhantseva, Genericity of Howson's  property of finitely presented groups,
International Algebraic Conference dedicated to the memory of  D.K. Faddeev, Saint-Petersburg, Russia, 24-30 June, 1997. Abstracts, 158-159. 

 G.N. Arzhantseva, Generic classes of finitely presented groups,
International Conference "Modern problems of Number Theory and Applications", Tula, Russia, 9-14 September, 1996, Abstracts,  p.9.

 G.N. Arzhantseva, Generic classes of finitely presented groups,
International Conference "Mathematics. Modeling. Ecology" Volgograd, Russia, 27-31 May, 1996. Abstracts, p.23.