Geometry & Topology

On knot Floer homology in double branched covers

Lawrence Roberts

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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.

Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 413-467.

Dates
Received: 4 November 2007
Revised: 1 November 2011
Accepted: 20 October 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732528

Digital Object Identifier
doi:10.2140/gt.2013.17.413

Mathematical Reviews number (MathSciNet)
MR3035332

Zentralblatt MATH identifier
06152267

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57R58: Floer homology

Keywords
knot Floer homology Khovanov homology branched double cover

Citation

Roberts, Lawrence. On knot Floer homology in double branched covers. Geom. Topol. 17 (2013), no. 1, 413--467. doi:10.2140/gt.2013.17.413. https://projecteuclid.org/euclid.gt/1513732528


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