© | << < ? > >> | Dror Bar-Natan: Talks:

Khovanov Homology for Tangles and Cobordisms

Colloquium, University of Toronto

SS5017, 4PM, December 8, 2004

Abstract. In my talk I will display one complicated picture and discuss it at length, finding that it's actually quite simple. Applying a certain 2D TQFT, we will get a homology theory whose Euler characteristic is the Jones polynomial. Not applying it, very cheaply we will get an invariant of tangles which is functorial under cobordisms and an invariant of 2-knots.

Why is it interesting?

Prerequisites. Not to be scared of the words "category" and "functor" and the phrase "a homotopy between chain complexes". Otherwise all will be explained.

The picture:

The Main Picture

Handouts: MoreFormulas.pdf. NewHandout-1.pdf,
Transparencies: Reid2Proof.pdf, R3Full.pdf, FrameRack.pdf.
See also my paper Khovanov's Homology for Tangles and Cobordisms.