Computations of the Ozsvath-Szabo knot concordance invariant

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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper19.abs.html

References in corpus (3)

• Knot Floer homology and the four-ball genus
• Bounds for the Thurston-Bennequin number from Floer homology
• Splitting the concordance group of algebraically slice knots

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• New topologically slice knots
• Ozsvath-Szabo and Rasmussen invariants of doubled knots
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• A note on the four-dimensional clasp number of knots
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• 3-braid knots with maximal 4-genus
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