Knot Floer homology in cyclic branched covers

Abstract

In this paper, we introduce a sequence of invariants of a knot K in S^3: the knot Floer homology groups of the preimage of K in the m-fold cyclic branched cover over K. We exhibit the knot Floer homology in the m-fold branched cover as the categorification of a multiple of the Turaev torsion in the case where the m-fold branched cover is a rational homology sphere. In addition, when K is a 2-bridge knot, we prove that the knot Floer homology of the lifted knot in a particular Spin^c structure in the branched double cover matches the knot Floer homology of the original knot K in S^3. We conclude with a calculation involving two knots with identical knot Floer homology in S^3 for which the knot Floer homology groups in the double branched cover differ as Z_2-graded groups.

This is the version published by Algebraic & Geometric Topology on 25 September 2006

References in corpus (2)

• Heegaard Floer homology and alternating knots
• Floer homology of surgeries on two-bridge knots

Cited by in corpus (7)

• Knot Floer homology detects fibred knots
• On knot Floer homology in double branched covers
• A flexible construction of equivariant Floer homology and applications
• Knot concordance and Heegaard Floer homology invariants in branched covers
• Computing Knot Floer Homology in Cyclic Branched Covers
• A rank inequality for the knot Floer homology of double branched covers
• On concordances in 3-manifolds