Local Khovanov homology Talk 1

From ScottWiki

I'll start talking about Bar-Natan's version of Khovanov homology, and see how far we get. I'm no expert on these things, so I might not have much to say! However, what I will say, I'll say slowly, so hopefully everyone will understand. Khovanov homology is a better version of the Jones polynomial -- in particular, it's a (graded) homology theory for knots and links, whose (graded) Euler characteristic is the Jones polynomial. It's an example of 'categorification' -- and Bar-Natan's version makes this particularly clear; instead of just pictures of knots, this talk will have pretty (!) pictures of cobordisms between knots.

There are mysterious connections with sl_n representation theory and knot Floer homology, but I promise not to mention these!