A combinatorial description of knot Floer homology

Abstract

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.

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

References in corpus (3)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Heegaard Floer homology and alternating knots

Cited by in corpus (4)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Cables of thin knots and bordered Heegaard Floer homology
• Khovanov homology, sutured Floer homology, and annular links
• Grid Diagrams and Legendrian Lens Space Links