A rank inequality for the knot Floer homology of double branched covers

Abstract

Given a knot K in S^3, let Σ(K) be the double branched cover of S^3 over K. We show there is a spectral sequence whose E^1 page is (\hat{HFK}(Σ(K), K) \otimes V^{n-1}) \otimes \mathbb Z_2((q)), for V a \mathbb Z_2-vector space of dimension two, and whose E^{\infty} page is isomorphic to (\hat{HFK}(S^3, K) \otimes V^{n-1}) \otimes \mathbb Z_2((q)), as \mathbb Z_2((q))-modules. As a consequence, we deduce a rank inequality between the knot Floer homologies \hat{HFK}(Σ(K), K) and \hat{HFK}(S^3, K).

This is the final version as published by Algebraic & Geometric Topology (and posted here by the author)

References in corpus (3)

• Floer homology and knot complements
• Knot Floer homology detects fibred knots
• Hamiltonian handleslides for Heegaard Floer homology

Cited by in corpus (9)

• A flexible construction of equivariant Floer homology and applications
• DG structures on odd categorified quantum sl(2)
• A rank inequality for the annular Khovanov homology of 2-periodic links
• Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
• Rank inequalities for the Heegaard Floer homology of branched covers
• Localization in Khovanov homology
• Equivariant Lagrangian Floer cohomology via semi-global Kuranishi structures
• Equivariant Floer theory and double covers of three-manifolds
• Involutions, knots, and Floer K-theory