Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Computations of the Ozsváth–Szabó knot concordance invariant

Charles Livingston

Geometry & Topology 8 (2004) 735–742

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