Khovanov homology, sutured Floer homology, and annular links

Abstract

Lawrence Roberts, extending the work of Ozsvath-Szabo, showed how to associate to a link, L, in the complement of a fixed unknot, B, in S^3, a spectral sequence from the Khovanov homology of a link in a thickened annulus to the knot Floer homology of the preimage of B inside the double-branched cover of L. In a previous paper, we extended Ozsvath-Szabo's spectral sequence in a different direction, constructing for each knot K in S^3 and each positive integer n, a spectral sequence from Khovanov's categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology of a reduced n-cable of K. In the present work, we reinterpret Roberts' result in the language of Juhasz's sutured Floer homology and show that our spectral sequence is a direct summand of Roberts'.

23 pages, 7 figures; This is the published version. Important note: In the statement of Theorem 3.1 appearing in v.1, the "only if" direction of the final sentence is FALSE. This has been corrected in v.2. We are grateful to Matt Hedden for pointing out the mistake

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• On Khovanov-Seidel quiver algebras and bordered Floer homology
• Sutured Khovanov homology distinguishes braids from other tangles
• Sutured Khovanov homology, Hochschild homology, and the Ozsvath-Szabo spectral sequence
• An action of gl(1|1) on odd annular Khovanov homology
• Sutured annular Khovanov homology and two periodic braids