Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers

2006/10/09 by J. Elisenda Grigsby, Grigsby, J. Elisenda
Mathematics · #57M12 #57M27 #57R58 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0610238

openalex publication_date 2006/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants

Related

• Combinatorial knot Floer homology and cyclic branched covers
• Braids and combinatorial knot Floer homology
• Computations of Heegaard-Floer knot homology
• A combinatorial description of knot Floer homology
• Algebras with matchings and knot Floer homology