A combinatorial description of knot Floer homology

Ciprian Manolescu, Peter Ozsváth, Sucharit Sarkar

Research output: Contribution to journalArticlepeer-review

101 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)633-660
Number of pages28
JournalAnnals of Mathematics
Issue number2
StatePublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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