On knot Floer homology in double branched covers

Roberts, Lawrence

doi:10.2140/gt.2013.17.413

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On knot Floer homology in double branched covers

Lawrence P Roberts

Geometry & Topology 17 (2013) 413–467

DOI: 10.2140/gt.2013.17.413

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 $S^{3}$ , and $Y$ is the double cover of $S^{3}$ branched over a link, we relate the $E^{2}$ –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

Volume 17, issue 1 (2013)