Topology Seminar (Main Talk): Instanton knot homology and equivariant gauge theory

Seminar | October 7 | 4:10-5 p.m. | 3 Evans Hall

 Nikolai Saveliev, University of Miami

 Department of Mathematics

The instanton knot homology is a Floer theory recently defined by Kronheimer and Mrowka using gauge theory on orbifolds; it has been instrumental in proving that the Khovanov homology is an unknot detector. We show how replacing gauge theory on an orbifold with an equivariant gauge theory on its double branched cover simplifies the matters and allows for explicit calculations for several classes of knots. This is a joint project with Prayat Poudel.