Friday, May 18, 2018
Building 15, Room 104
Geometry and Topology Seminar
Surgery, Polygons and Instanton Floer homology
Yi Xie, Simons Center for Geometry and Physics, SUNY Stony Brook
Many classical numerical invariants (including Casson invariant, Alexander polynomial and Jones polynomial) for 3-manifolds or links satisfy surgery formulas relating three different 3-manifolds or links. All those invariants are categorified by certain Floer homologies (or Khovanov homology) which also satisfy so-called surgery exact triangles. In this talk I will discuss the notion of "surgery exact polygons" which appears in the SU(N)-instanton Floer homology theory. Roughly speaking, an "n-gon" is a relation among the Floer homology groups of 3-manifolds obtained by n different Dehn surgeries on a fixed knot. It generalizes the surgery exact triangle in SU(2)-instanton Floer homology. If time permits, I will also talk about a homological-mirror-symmetry-type conjecture which motivates this work. This is joint work with Lucas Culler and Aliakbar Daemi.