Geometry & Topology, Vol. 8 (2004)
Paper no. 19, pages 735--742.
Computations of the Ozsvath-Szabo knot concordance invariant
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.
Concordance, knot genus, Slice-Bennequin Inequality
AMS subject classification.
Secondary: 57M25, 57Q60.
Submitted to GT on 20 Febrary 2004.
Paper accepted 29 April 2004.
Paper published 17 May 2004.
Notes on file formats
Department of Mathematics, Indiana University
Bloomington, IN 47405, USA
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