Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Khovanov homology is a 'categorification' of the Jones polynomial: it associates a (doubly-graded) vector space to each link. Just as the Jones polynomial is the essential ingredient in defining the Witten-Reshetikhin-Turaev invariants of 3-manifolds, I'll explain how Khovanov homology can be used to define an invariant of a smooth 4-manifold. There are some difficulties --- a fact about Khovanov homology that requires us to work mod 2 for now, and a somewhat involved story before we can precisely relate what we're doing to the Jones polynomial situation. Happily, though, the construction itself is fairly straightforward and elementary, and I'll spend most of the talk drawing pictures to explain this. (Joint work with Chris Douglas and Kevin Walker.)