Orateur: Krzysztof Putyra (EPFZ)
Titre:  Quantum Link Homology via Trace Functor.

Résumé: Trace functors are algebraic analogues of gluing together components of the boundary a of manifold. In particular, one can produce a TQFT functor for cobordisms embedded into a surface bundle M with fiber F from an extended TQFT for cobordisms with corners in F x I. In my talk I will discuss an application of this construction to link homology. Chen and Khovanov assigned a chain complex to a tangle in a thickened plane, and we have shown that Hochschild homology of this chain complex recovers the Asaesa-Przytycki-Sikora invariant for links in a thickened annulus. I will describe how to deform the Hochschild homology to obtain a richer invariant, which we call the quantum link homology. This new homology admits an action of the quantum group Uq(sl_2) and is projectively functorial with respect to link cobordisms, leading to invariants of knotted surfaces in 4D. We provide evidence that this invariant is non-trivial. This is a joint work with Anna Beliakova (University of Zurich) and Stephan Wehrli (Syracuse University). Reference: arXiv:1605.03523