Order in the concordance group and Heegaard Floer homology

Jabuka, Stanislav; Naik, Swatee

doi:10.2140/gt.2007.11.979

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Order in the concordance group and Heegaard Floer homology

Stanislav Jabuka and Swatee Naik

Geometry & Topology 11 (2007) 979–994

DOI: 10.2140/gt.2007.11.979

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

Volume 11, issue 2 (2007)