MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

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Funded by The Danish National Research Foundation

Geometric Mathematical Physics Seminar

Abstract
This talk will be an introduction to a homology theory of links, invented by Mikhail Khovanov in 1999. It associates to every link diagram a bigraded chain complex whose graded Euler characteristic is the Jones polynomial. The chain complex is invariant up to chain equivalence under Reidemeister moves, so the isomorphism classes of the associated homology groups are link invariants. These invariants are stronger than the Jones polynomial. Also, Khovanov homology is a functor. Namely, any link cobordism induces a homomorphism between the homology groups of its boundary links, which is invariant (up to sign) under ambient isotopy of the link cobordism. This latter statement comes with an important caveat, which also will be mentioned in the talk, if time permits.

Contact person:Jørgen Ellegaard Andersen.