## Geometry & Topology

### On knot Floer homology in double branched covers

Lawrence Roberts

#### 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
Revised: 1 November 2011
Accepted: 20 October 2012
First available in Project Euclid: 20 December 2017

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

#### 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