English

A combinatorial spanning tree model for knot Floer homology

Geometric Topology 2022-04-12 v3 Symplectic Geometry

Abstract

We iterate Manolescu's unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over Z/2Z\mathbb{Z}/2\mathbb{Z}. The result is a spectral sequence which converges to a stabilized version of delta-graded knot Floer homology. The (E2,d2)(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.

Keywords

Cite

@article{arxiv.1105.5199,
  title  = {A combinatorial spanning tree model for knot Floer homology},
  author = {John A. Baldwin and Adam Simon Levine},
  journal= {arXiv preprint arXiv:1105.5199},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-21T18:12:52.458Z