Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers

Details Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers

2006-10-09

arxiv.org/abs/math/0610238v2

Mathematics

Geometric Topology

20 pages, 14 figures; Minor expositional improvements, typos corrected throughout (most seriously, the x,y coordinates used in

Scientific paper

We introduce a simple combinatorial method for computing all versions of the knot Floer homology of the preimage of a two-bridge knot K(p,q) inside its double-branched cover, -L(p,q). The 4-pointed genus 1 Heegaard diagram we obtain looks like a twisted version of the toroidal grid diagrams recently introduced by Manolescu, Ozsvath, and Sarkar. We conclude with a discussion of how one might obtain nice Heegaard diagrams for cyclic branched covers of more general knots.

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