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

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

2011-07-11

arxiv.org/abs/1107.2154v2

Mathematics

Geometric Topology

Corrected an error in Corollary 1.3 (now split into Corollaries 1.3 and 1.4). Corrected typos

Scientific paper

Given a knot K in S^3, let \Sigma(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}(\Sigma(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}(\Sigma(K), K) and \hat{HFK}(S^3, K).

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