Combinatorial link Floer homology
Dylan Thurston, Barnard College, Columbia University

We give a completely combinatorial definition and proof of invariance
of Heegaard-Floer homology for links in the 3-sphere. Heegaard-Floer
homology is a fairly recent link and manifold invariant that, among
other uses, detects the genus of a knot and whether or not it fibers.
As a result, we get the world's simplest algorithm for finding the
knot genus, the complexity of the simplest oriented surface whose
boundary is a given knot. The combinatorial definition is based on a
grid-link presentation of the link, also known as an arc
presentation.

This talk is work of or joint work with Ng, Manolescu, Ozsváth,
Sarkar, and Szabó.

Colloquium, Department of Mathematics, Rice University
November 15, 2007 4:00-5:00 PM, HB 227


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