Holomorphic flexibility of complex manifolds


Dror Bar-Nathan

University of Toronto

Harvard University

Thursday, October 28, 2004


Talk at 4:30 p.m. in Science Center D

Tea at 4:00 p.m. in the Math Lounge


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?

  • It has several generalizations, but as a whole, we hardly understand it. It may have significant algebraic and/or physical ramifications. In fact, it suggests that much of algebra as we know it (or at least quantum algebra as we know it), is a shadow of some "higher algebra".

  • It is a knot/link/tangle invariant stronger than the Jones polynomial, and an invariant of 2-knots in 4-space.

  • It seems stronger than the original "Khovanov Homology".

  • It is functorial in the appropriate sense, and Rasmussen (math.GT/0402131) uses it to do some real topology.

The picture:


The Main Picture


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Posted: March 10, 2004    URL: