Computations of the Ozsváth–Szabó knot concordance invariant

Livingston, Charles

doi:10.2140/gt.2004.8.735

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Computations of the Ozsváth–Szabó knot concordance invariant

Charles Livingston

Geometry & Topology 8 (2004) 735–742

DOI: 10.2140/gt.2004.8.735

arXiv: math.GT/0311036

Abstract

Ozsváth and Szabó have defined a knot concordance invariant $τ$ that bounds the 4–ball genus of a knot. Here we discuss shortcuts to its computation. We include examples of Alexander polynomial one knots for which the invariant is nontrivial, including all iterated untwisted positive doubles of knots with nonnegative Thurston–Bennequin number, such as the trefoil, and explicit computations for several 10 crossing knots. We also note that a new proof of the Slice–Bennequin Inequality quickly follows from these techniques.

Keywords

concordance, knot genus, Slice–Bennequin Inequality

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M25, 57Q60

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Publication

Received: 20 2004

Accepted: 29 April 2004

Published: 17 May 2004

Proposed: Peter Ozsváth

Seconded: Joan Birman, Ronald Fintushel

Authors

Charles Livingston
Department of Mathematics Indiana University Bloomington Indiana 47405 USA

Volume 8, issue 2 (2004)