Algebraic & Geometric Topology

Computing knot Floer homology in cyclic branched covers

Adam Simon Levine

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Abstract

We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot KS3 in its m–fold cyclic branched cover Σm(K), and we give computations when m=2 for over fifty three-bridge knots with up to eleven crossings.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 2 (2008), 1163-1190.

Dates
Received: 9 December 2007
Revised: 4 March 2008
Accepted: 5 March 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796859

Digital Object Identifier
doi:10.2140/agt.2008.8.1163

Mathematical Reviews number (MathSciNet)
MR2443111

Zentralblatt MATH identifier
1160.57010

Subjects
Primary: 57R58: Floer homology
Secondary: 57M12: Special coverings, e.g. branched 57M27: Invariants of knots and 3-manifolds

Keywords
Knot Floer homology Branched cover

Citation

Levine, Adam Simon. Computing knot Floer homology in cyclic branched covers. Algebr. Geom. Topol. 8 (2008), no. 2, 1163--1190. doi:10.2140/agt.2008.8.1163. https://projecteuclid.org/euclid.agt/1513796859


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