Instaton Homology for Knots and Webs
Channel: UMD Mathematics
Date: 23/04/2013

Peter Kronheimer
William Casper Graustein Professor of Mathematics
Harvard University

ABSTRACT

Andreas Floer introduced instanton homology for 3-manifolds in the mid 1980's. He also described a variant he called knot homology, for knots in 3-manifolds. There has now been a lot of progress in understanding the structure of instanton knot homology and its relationship with other, more recent invariants of knots, such as Khovanov homology. Applications have included a proof that Khovanov homology detects the unknot. Replacing the Lie group SU(2) in Floer's construction with SU(N) for larger N leads to an invariant of "webs" (labeled trivalent graphs), with a connection to Khovanov-Rozansky homology. This talk will review some of these developments.

Recorded April 14th, 2013 as part of Calabifest: The 28th Geometry Festival.