Geometry & Topology

Computations of the Ozsváth–Szabó knot concordance invariant

Charles Livingston

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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.

Article information

Geom. Topol., Volume 8, Number 2 (2004), 735-742.

Accepted: 29 April 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57Q60: Cobordism and concordance

concordance knot genus Slice–Bennequin Inequality


Livingston, Charles. Computations of the Ozsváth–Szabó knot concordance invariant. Geom. Topol. 8 (2004), no. 2, 735--742. doi:10.2140/gt.2004.8.735.

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