Geometry and Topology Seminar: Ring structures in singular instanton Floer homology

Abstract: In this talk, I will present a complete characterization of the ring structure of the singular instanton homology of S^1 times a punctured surface (in C-coefficients).  This ring structure gives all the universal relations of the module structures of instanton Floer homology groups.  Earlier partial results on this ring have yielded a large number of topological applications, including detection results on Khovanov homology and new results on the SU(2) representation variety of link complements.  I will also discuss some of these topological applications.  This talk is based on joint works with Yi Xie.

Host: Minh Nguyen