A combinatorial spanning tree model for knot Floer homology

Abstract

We iterate Manolescu's unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over $\mathbb{Z}/2\mathbb{Z}$. The result is a spectral sequence which converges to a stabilized version of delta-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.

58 pages, 18 figures. Published version, with updated references

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Cited by in corpus (19)

• Khovanov module and the detection of unlinks
• On the equivalence of Legendrian and transverse invariants in knot Floer homology
• A contact invariant in sutured monopole homology
• Sutured Floer homology and invariants of Legendrian and transverse knots
• Totally Twisted Khovanov Homology
• Two-fold quasi-alternating links, Khovanov homology and instanton homology
• On the equivalence of contact invariants in sutured Floer homology theories
• Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies
• Peculiar modules for 4-ended tangles
• Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology
• On symmetries of peculiar modules; or, $\delta$-graded link Floer homology is mutation invariant
• An alternating labeling on a spanning tree of Seifert graphs and applications in knot theory
• Kauffman states and Heegaard diagrams for tangles
• Kauffman's clock lattice as a graph of perfect matchings: a formula for its height
• Skein relations for tangle Floer homology
• Earrings, sutures and pointed links
• Twisted skein homology
• On the homology theory for the chromatic polynomials
• Khovanov homology and binary dihedral representations for marked links