Volume 17, issue 1 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
On knot Floer homology in double branched covers

Lawrence P Roberts

Geometry & Topology 17 (2013) 413–467
Abstract

We define a link surgery spectral sequence for each knot Floer homology group for a knot, K, in a three manifold, Y . When K arises as the double cover of an unknot in S3, and Y is the double cover of S3 branched over a link, we relate the E2–page to a version of Khovanov homology for links in an annulus defined by Asaeda, Przytycki and Sikora. Finally we examine the specific cases when the branch locus is a braid, and when it is alternating.

Keywords
knot Floer homology, Khovanov homology, branched double cover
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R58
References
Publication
Received: 4 November 2007
Revised: 1 November 2011
Accepted: 20 October 2012
Published: 12 March 2013
Proposed: Peter S. Ozsváth
Seconded: Ronald Fintushel, Ronald Stern
Authors
Lawrence P Roberts
Department of Mathematics
University of Alabama
Tuscaloosa, AL 35487-0350
USA
http://www.bama.ua.edu/~lproberts