Some geometric constructions of link homology
Abstract
Triply graded link homology (introduced by Khovanov and Rozansky) is a
categorification of the HOMFLYPT polynomial. In this talk I will discuss
recent joint work with Ben Webster which gives a geometric construction of this invariant in terms of equivariant constructible sheaves. In this
framework the Reidemeister moves have quite natural geometric proofs. A
generalisation of this construction yields a categorification of the
coloured HOMFLYPT polynomial, constructed (conjecturally) by Mackay, Stosic and Vaz. I will also describe how this approach leads to a natural formula for the Jones-Ocneanu trace in terms of the intersection cohomology of Schubert varieties in the special linear group.