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

Abstract

Given a diagram of a link K in S^3, we write down a Heegaard diagram for the branched-double cover Sigma(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 \hat{HF}(Sigma(K)) as a graded group. We also conjecture the existence of a delta-grading on \hat{HF}(Sigma(K)) analogous to the delta-grading on knot Floer and Khovanov homology.

43 pages, 20 figures

References in corpus (4)

• Floer homology and knot complements
• Computing Knot Floer Homology in Cyclic Branched Covers
• Lattice cohomology of normal surface singularities
• A spanning tree model for Khovanov homology

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