arXiv:math/0607691 Abstract

arXiv:math/0607691 [math.GT]Abstract References Reviews Resources

A combinatorial description of knot Floer homology

Ciprian Manolescu, Peter Ozsvath, Sucharit Sarkar

Published 2006-07-26, updated 2007-08-23Version 2

Given a grid presentation of a knot (or link) K in the three-sphere, we describe a Heegaard diagram for the knot complement in which the Heegaard surface is a torus and all elementary domains are squares. Using this diagram, we obtain a purely combinatorial description of the knot Floer homology of K.

Comments: 22 pages; 9 figures. Expanded proof of Proposition 2.3 and corrected typeos

Categories: math.GT, math.SG

Subjects: 57R58, 57M25

Keywords: knot floer homology, elementary domains, grid presentation, heegaard surface, knot complement

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