A combinatorial spanning tree model for knot Floer homology

John A. Baldwin; Adam Simon Levine

doi:10.1016/j.aim.2012.06.006

A combinatorial spanning tree model for knot Floer homology

John A. Baldwin, Adam Simon Levine

Mathematics

Research output: Contribution to journal › Article › peer-review

29 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 language	English (US)
Pages (from-to)	1886-1939
Number of pages	54
Journal	Advances in Mathematics
Volume	231
Issue number	3-4
DOIs	https://doi.org/10.1016/j.aim.2012.06.006
State	Published - Oct 2012

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

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

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10.1016/j.aim.2012.06.006

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title = "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 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.",

keywords = "Exact triangle, Heegaard Floer homology, Khovanov homology, Knot Floer homology, Spanning tree",

author = "Baldwin, {John A.} and Levine, {Adam Simon}",

note = "Funding Information: Both authors were partially supported by NSF Postdoctoral Fellowships . ",

year = "2012",

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T1 - A combinatorial spanning tree model for knot Floer homology

AU - Baldwin, John A.

AU - Levine, Adam Simon

N1 - Funding Information: Both authors were partially supported by NSF Postdoctoral Fellowships .

PY - 2012/10

Y1 - 2012/10

N2 - 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.

AB - 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.

KW - Exact triangle

KW - Heegaard Floer homology

KW - Khovanov homology

KW - Knot Floer homology

KW - Spanning tree

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EP - 1939

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 3-4

ER -

A combinatorial spanning tree model for knot Floer homology

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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