A combinatorial spanning tree model for knot Floer homology

John A. Baldwin; Adam Simon Levine

doi:10.1016/j.aim.2012.06.006

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arXiv · 1105.5199

A combinatorial spanning tree model for knot Floer homology

John A. Baldwin·Adam Simon Levine

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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.

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John A. Baldwin, Adam Simon Levine. 2011-05-26. A combinatorial spanning tree model for knot Floer homology. https://doi.org/10.1016/j.aim.2012.06.006

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