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

Kristen Hendricks

Algebraic & Geometric Topology 12 (2012) 2127–2178
Abstract

Given a knot K in S3, let Σ(K) be the double branched cover of S3 over K. We show there is a spectral sequence whose E1 page is (HFK̂(Σ(K),K) V (n1)) 2((q)), for V a 2–vector space of dimension two, and whose E page is isomorphic to (HFK̂(S3,K) V (n1)) 2((q)), as 2((q))–modules. As a consequence, we deduce a rank inequality between the knot Floer homologies HFK̂(Σ(K),K) and HFK̂(S3,K).

Keywords
Heegaard Floer, double branched covers, knot theory, Floer cohomology, localization
Mathematical Subject Classification 2010
Primary: 53D40, 57M25, 57M27, 57R58
References
Publication
Received: 11 July 2011
Revised: 18 June 2012
Accepted: 12 July 2012
Published: 26 December 2012
Authors
Kristen Hendricks
Department of Mathematics
Columbia University
2990 Broadway
New York NY 10027
USA
http://math.columbia.edu/~hendricks/