A combinatorial description of knot Floer homology

@article{Manolescu2006ACD,
  title={A combinatorial description of knot Floer homology},
  author={C. Manolescu and P. Ozsv'ath and S. Sarkar},
  journal={Annals of Mathematics},
  year={2006},
  volume={169},
  pages={633-660}
}
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. 
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