EVENT DETAILS AND ABSTRACT

Title: An Introduction to Khovanov Homology
Speaker: Louis Kauffman
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:

This talk is an elementary introduction to Khovanov homology. We review the construction of the bracket model for the Jones polynomial as a state summation, and then show how one can make the set of states into a category with a naturally associated chain complex. The homology of this chain complex is the Khovanov homoloogy. A natural category of surface cobordisms describes the maps in the chain complex. Khovanov homology is a significant extension of the Jones polynomial. The Jones polynomial itself is a graded Euler characteristic of the Khovanov homology and recently, Kronheimer and Mrowka have proved that Khovanov homology can detect the unknot. The corresponding conjecture that the Jones polynomial detects the unknot remains open.