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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- July 2006
- arXiv:
- arXiv:math/0607691
- Bibcode:
- 2006math......7691M
- Keywords:
-
- Mathematics - Geometric Topology;
- Mathematics - Symplectic Geometry;
- 57R58;
- 57M25
- E-Print:
- 18 pages