Title: Khovanov homology for 4-manifolds
Speaker: Scott Morrison
Speaker Info: Australian National University
Special Note: Note the unusual date for the actual talk.
(Joint work with Kevin Walker) I'll describe our attempts to define Khovanov homology for 4-manifolds. We beginning by constructing a `disklike 4-category' from Khovanov homology. There are certain technical difficulties, and for now we're forced to work in characteristic 2. From there, we follow the standard topological field theory recipe to construct vector space valued invariants of 4-manifolds (possibly with boundary, possibly with a link in the boundary). Along the way, however, this construction loses some of the nice properties of Khovanov homology, in particular the exact triangle for resolving a crossing in a link. Our recent work on the blob complex began as an attempt to remedy this defect, and I'll describe the computational tool that the blob complex provides in this context.Date: Friday, November 16, 2012