Dylan Thurston (Columbia University)
Combinatorial link Floer homology
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 with Ng, Manolescu, Ozsváth, Sarkar, and Szabó.
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