Topology Seminar (Main Talk): A sheaf-theoretic model for $SL(2,\mathbb C)$ Floer homology

Seminar | March 21 | 4-5 p.m. | 3 Evans Hall

 Ciprian Manolescu, UCLA

 Department of Mathematics

I will explain the construction of a new homology theory for three-manifolds, defined using perverse sheaves on the $SL(2,\mathbb C)$ character variety. Our invariant is a model for an $SL(2,\mathbb C)$ version of Floer's instanton homology. I will present a few explicit computations for Brieskorn spheres, and discuss the connection to the Kapustin-Witten equations and Khovanov homology. This is joint work with Mohammed Abouzaid.