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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