Geometry & Topology

Knot concordance and Heegaard Floer homology invariants in branched covers

J Elisenda Grigsby, Daniel Ruberman, and Sašo Strle

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Abstract

By studying the Heegaard Floer homology of the preimage of a knot K⊂S3 inside its double branched cover, we develop simple obstructions to K having finite order in the classical smooth concordance group. As an application, we prove that all 2–bridge knots of crossing number at most 12 for which the smooth concordance order was previously unknown have infinite smooth concordance order.

Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 2249-2275.

Dates
Received: 1 February 2007
Revised: 24 June 2008
Accepted: 13 June 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800126

Digital Object Identifier
doi:10.2140/gt.2008.12.2249

Mathematical Reviews number (MathSciNet)
MR2443966

Zentralblatt MATH identifier
1149.57007

Subjects
Primary: 57R58: Floer homology 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M12: Special coverings, e.g. branched 57M27: Invariants of knots and 3-manifolds

Keywords
Smooth knot concordance Heegaard Floer homology branched covers Knot concordance branched cover $\tau$–invariant

Citation

Grigsby, J Elisenda; Ruberman, Daniel; Strle, Sašo. Knot concordance and Heegaard Floer homology invariants in branched covers. Geom. Topol. 12 (2008), no. 4, 2249--2275. doi:10.2140/gt.2008.12.2249. https://projecteuclid.org/euclid.gt/1513800126


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