Volume 8, issue 2 (2004)

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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 $\tau$ 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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25, 57Q60