Orateur: Duncan
McCoy (Glasgow):
Titre: Alternating knots
with unknotting number one.
Résumé:
The unknotting number of a knot is defined to be the minimal number
of crossing changes requires in any diagram to obtain the unknot.
It can be shown that an alternating knot has unknotting number one if and
only if every alternating diagram contains an unknotting crossing. I will
explain the proof of this result which uses a Dehn Surgery obstruction,
originally due to Greene, arising from Donaldson's Theorem and Heegaard
Floer homology.