Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers
Geometric Topology
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0610238,
title = {Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers},
author = {J. Elisenda Grigsby},
journal= {arXiv preprint arXiv:math/0610238},
year = {2007}
}
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)