Geometric Analysis and Topology Seminar

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A Combinatorial Description of Knot Floer Homology

Speaker: Ciprian Manolescu, Columbia University

Location: Warren Weaver Hall 1013

Date: Friday, November 3, 2006, 1 p.m.

Synopsis:

Knot Floer homology is an invariant of knots in the three-sphere, which detects the genus of the knot, and can be used to recover the Heegaard Floer homology of any surgery on that knot. The original definition, due to Ozsvath-Szabo and Rasmussen, involved counts of pseudoholomorphic disks in a symplectic manifold. In joint work with Peter Ozsvath and Sucharit Sarkar, we found a purely combinatorial description of this invariant. Starting with a grid presentation of the knot, one construct a special Heegaard diagram for the knot complement, in which the count of pseudolomorphic disks is elementary.