EVENT DETAILS AND ABSTRACT

Title: Extension of Khovanov's homology to links in S2 x S1
Speaker: Lev Rozansky
Speaker Info: UNC
Brief Description:
Special Note:
Abstract:

Khovanov's homology categorifies the Jones polynomial, which is a polynomial invariant of links in a 3-sphere S3. The Jones polynomial can be extended to the Witten-Reshetikhin-Turaev (WRT) invariant of links in other 3-manifolds, but the WRT invariant is not a polynomial, and it is not clear how it should be categorified. However, the WRT invariant of links in S2 x S1 (and in connected sums of S2 x S1) has a `stable limit', which is a polynomial. I will explain how to categorify it by building a `mini-TQFT' in which to a 2-sphere with 2n punctures one associates a derived category of modules over Khovanov's ring H_n, to a (2n,2n)-tangle inside S2 x [0,1] one associates an H_n bimodule and to a closure of this tangle, which is a link in S2 x S1, one associates the Hochschild homology of this bimodule.