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Invariants of 4-manifolds from Khovanov homology
Geometry/Topology| Speaker: | Scott Morrison, UC Berkeley |
| Location: | 2212 MSB |
| Start time: | Tue, Jan 31 2012, 3:10PM |
Description
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.)