11/30/2006

Dylan Thurston
Columbia and Barnard

A combinatorial definition of Heegaard-Floor homology for links

We give a completely combinatorial definition and proof of invariance of Heegaard-Floer homology for links in the 3-sphere. The definition is based on a grid-link presentation of the link, also known as an arc presentation. In particular, this yields a simple algorithm for computing the knot genus. If time permits, we will describe how to extract invariants of Legendrian and transverse links in this homology.

Parts of this talk are work of Manolescu, Ozsváth, and Sarkar, and parts are joint work with Manolescu, Ozsváth, and Szabó.