# 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 $K$.

## Authors

Ciprian Manolescu

Department of Mathematics
Columbia University
New York NY, 10027
United States

Peter Ozsváth

Department of Mathematics
Columbia University
New York NY, 10027
United States

Sucharit Sarkar

Department of Mathematics
Princeton University
Princeton, NJ 08544
United States