Geometry and Topology Seminar
Monday, November 27, 2017 at 3:00pm to 4:00pm
Aliakbar Daemi (Stony Brook)
Title: Surgery, Polygons and Unitary Representations
Abstract: Given a framed knot in a 3-manifold, one can use Dehn surgery to construct new 3-manifolds. There are several surgery exact triangles which give relations among the Floer homological invariants of 3-manifolds obtained by Dehn surgery on a knot. Such exact triangles provide important tools in studying 3-manifold Floer homologies. In his pioneering work, Floer constructed an exact triangle which generalizes the surgery formula for Casson's invariant. This surgery exact triangle motivates similar exact triangles in several other Floer homology theories such as Monopole Floer homology and Heegaard Floer homology. A few years ago, Kronheimer and Mrowka extended the definition of instanton homology by replacing the Lie group U(2) with U(N). In this talk, I’ll explain how Floer’s surgery exact triangle generalizes to ``surgery exact polygons’’ for U(N)-instanton homology. This talk is based on a joint work with Lucas Culler and Yi Xie.