Computing Knot Floer Homology in Cyclic Branched Covers

Abstract

We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot K in its m-fold cyclic branched cover Sigma^m(K), and we give computations when m=2 for over fifty three-bridge knots with up to eleven crossings.

30 pages, 2 figures, 1 long table. Added computations in Section 5; rewrote Section 6; corrected typos and minor mistakes

References in corpus (4)

• Floer homology and knot complements
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Combinatorial Description of Knot Floer Homology of Cyclic Branched Covers
• Covering spaces and Q-gradings on Heegaard Floer homology

Cited by in corpus (9)

• A spanning tree model for the Heegaard Floer homology of a branched double-cover
• A flexible construction of equivariant Floer homology and applications
• A rank inequality for the knot Floer homology of double branched covers
• On concordances in 3-manifolds
• A combinatorial description of the $U^2=0$ version of Heegaard Floer homology
• Embedded and Lagrangian Knotted Tori in $\BR^4$ and Hypercube Homology
• Upsilon invariants from cyclic branched covers
• Combinatorial knot Floer homology and cyclic branched covers
• Combinatorial knot Floer homology and cyclic double branched covers