Volume 17, issue 5 (2017)

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The topological sliceness of $3$–strand pretzel knots

Allison N Miller

Algebraic & Geometric Topology 17 (2017) 3057–3079

We give a complete characterization of the topological slice status of odd 3–strand pretzel knots, proving that an odd 3–strand pretzel knot is topologically slice if and only if it either is ribbon or has trivial Alexander polynomial. We also show that topologically slice even 3–strand pretzel knots, except perhaps for members of Lecuona’s exceptional family, must be ribbon. These results follow from computations of the Casson–Gordon 3–manifold signature invariants associated to the double branched covers of these knots.

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knot concordance, pretzel knots
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57N70
Received: 1 November 2016
Revised: 15 April 2017
Accepted: 13 June 2017
Published: 19 September 2017
Allison N Miller
Department of Mathematics
University of Texas
Austin, TX
United States