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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Knot concordance and Heegaard Floer homology invariants in branched covers

J Elisenda Grigsby, Daniel Ruberman and Sašo Strle

Geometry & Topology 12 (2008) 2249–2275
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.

Keywords
Smooth knot concordance, Heegaard Floer homology, branched covers, Knot concordance, branched cover, $\tau$–invariant
Mathematical Subject Classification 2000
Primary: 57R58, 57M25
Secondary: 57M12, 57M27
References
Publication
Received: 1 February 2007
Revised: 24 June 2008
Accepted: 13 June 2008
Published: 2 September 2008
Proposed: Tomasz Mrowka
Seconded: Ronald Stern, Peter Ozsváth
Authors
J Elisenda Grigsby
Department of Mathematics
Columbia University
2990 Broadway MC4406
New York
NY 10027
USA
Daniel Ruberman
Department of Mathematics
MS 050
Brandeis University
Waltham
MA 02454
USA
Sašo Strle
Faculty of Mathematics and Physics
University of Ljubljana
Jadranska 21
1000 Ljubljana
Slovenia