Volume 11, issue 2 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Order in the concordance group and Heegaard Floer homology

Stanislav Jabuka and Swatee Naik

Geometry & Topology 11 (2007) 979–994
Abstract

We use the Heegaard–Floer homology correction terms defined by Ozsváth–Szabó to formulate a new obstruction for a knot to be of finite order in the smooth concordance group. This obstruction bears a formal resemblance to that of Casson and Gordon but is sensitive to the difference between the smooth versus topological category. As an application we obtain new lower bounds for the concordance order of small crossing knots.

Keywords
concordance order, Heegaard Floer homology
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57R58
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Publication
Received: 20 November 2006
Revised: 6 February 2007
Accepted: 30 January 2007
Published: 30 May 2007
Proposed: Ron Stern
Seconded: Peter Teichner and Peter Ozsváth
Authors
Stanislav Jabuka
Department of Mathematics and Statistics
University of Nevada
Reno NV 89557
USA
Swatee Naik
Department of Mathematics and Statistics
University of Nevada
Reno NV 89557
USA