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

Hendricks, Kristen¹

¹Department of Mathematics, Columbia University, 2990 Broadway, New York NY 10027, USA

Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2127-2178

Résumé

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 ⊗(n−1)) ⊗ ℤ2((q)), for V a ℤ2–vector space of dimension two, and whose E∞ page is isomorphic to (HFK̂(S3,K) ⊗ V ⊗(n−1)) ⊗ ℤ2((q)), as ℤ2((q))–modules. As a consequence, we deduce a rank inequality between the knot Floer homologies HFK̂(Σ(K),K) and HFK̂(S3,K).

Détail

DOI : 10.2140/agt.2012.12.2127

Classification : 53D40, 57M25, 57M27, 57R58
Keywords: Heegaard Floer, double branched covers, knot theory, Floer cohomology, localization

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