A combinatorial spanning tree model for knot Floer homology

John A. Baldwin, Adam Simon Levine

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We iterate Manolescu's unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over Z/2Z. The result is a spectral sequence which converges to a stabilized version of δ-graded knot Floer homology. The (E 2, d 2) page of this spectral sequence is an algorithmically computable chain complex expressed in terms of spanning trees, and we show that there are no higher differentials. This gives the first combinatorial spanning tree model for knot Floer homology.

Original languageEnglish (US)
Pages (from-to)1886-1939
Number of pages54
JournalAdvances in Mathematics
Volume231
Issue number3-4
DOIs
StatePublished - Oct 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Exact triangle
  • Heegaard Floer homology
  • Khovanov homology
  • Knot Floer homology
  • Spanning tree

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