Geometry & Topology, Vol. 8 (2004) Paper no. 19, pages 735--742.

Computations of the Ozsvath-Szabo knot concordance invariant

Charles Livingston

Abstract. Ozsvath and Szabo have defined a knot concordance invariant tau 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

AMS subject classification. Primary: 57M27. Secondary: 57M25, 57Q60.

DOI: 10.2140/gt.2004.8.735

E-print: arXiv:math.GT/0311036

Submitted to GT on 20 Febrary 2004. Paper accepted 29 April 2004. Paper published 17 May 2004.

Notes on file formats

Charles Livingston
Department of Mathematics, Indiana University
Bloomington, IN 47405, USA
Email: livingst@indiana.edu

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