A spanning tree model for the Heegaard Floer homology of a branched double-cover

2008/05/09 by Joshua Evan Greene, Joshua Greene · 1 citation
Computer Science · Mathematics · #Combinatorics #Conjecture #Floer homology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #math.GT

paper · pdf · doi:10.1112/jtopol/jtt007

43 pages, 20 figures

arxiv created 2008/05/09 · openalex publication_date 2013/03/29 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Given a diagram of a link K in S3, we write down a Heegaard diagram for the branched-double cover Σ(K). The generators of the associated Heegaard Floer chain complex correspond to Kauffman states of the link diagram. Using this model, we make some computations of the homology HF ^ ( Σ ( K ) ) as a graded group. We also conjecture the existence of a δ-grading on HF ^ ( Σ ( K ) ) analogous to the δ-grading on knot Floer and Khovanov homology.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Lattice cohomology of normal surface singularities
• Holomorphic disks and topological invariants for closed three-manifolds
• A categorification of the Jones polynomial
• An Introduction to Knot Theory
• A spanning tree model for Khovanov homology

Cited by

• The next-to-top term of the knot Floer homology of some non-fibered knots

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