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

Local Khovanov Homology - Computations and Mutations

Quantum Topology - Contemporary Issues and Perspectives

Utah, June 2005

Abstract. In the first two thirds of my talk I will describe local Khovanov Homology. If you've heard me talk about it before, you'll be bored and sleepy. If not, it's a very nice subject - the right way to view Khovanov homology, leading to simplifications, generalizations and computations which are otherwise difficult, impossible or unnatural.

In the last third of my talk I will describe my new and untested proof that Khovanov homology is invariant under knot mutation - bad news for some and good news for others. If you haven't thought about Khovanov homology before, you'll loose me now; otherwise, that's the time to wake up!

So now you can make an informed decision - sleep inside or sleep outside.

Handouts: LocalKh.pdf, ComputationsAndMutations.pdf.
Retraction of mutation invariance (added later): Mutation Invariance of Khovanov Homology.

Old title/abstract:

"New Stuff About Khovanov-Rozansky Homology"
"Local Khovanov Homology"

Abstract. If hard work will pay off, or luck will strike, then between now (May 13) and the conference I will have something new to say about Khovanov-Rozansky Homology. If so, this will be my subject. I'm holding my fingers crossed.

The more likely scenario is that I'll be talking about local Khovanov homology. I will explain how to localize Khovanov's link homology theory and get a theory which is more general, better at explaining things and yet computable much more easily. Please ignore those sleepy members of the audience who have heard me talk about this many times before, for sleep is contagious yet the subject really is lovely, and if you don't know all about it already, that's a great opportunity to learn.