J. Elisenda Grigsby
Published 2006-10-09, updated 2006-11-14Version 2
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.
Comments: 20 pages, 14 figures; Minor expositional improvements, typos corrected throughout (most seriously, the x,y coordinates used in discussion of intersection points beginning page 13 of previous version were incorrectly--but consistently--flipped)
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