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

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

2008-05-09

arxiv.org/abs/0805.1381v1

Mathematics

Geometric Topology

43 pages, 20 figures

Scientific paper

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.

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