The topological sliceness of 3–strand pretzel knots

Miller, Allison

doi:10.2140/agt.2017.17.3057

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The topological sliceness of $3$–strand pretzel knots

Allison N Miller

Algebraic & Geometric Topology 17 (2017) 3057–3079

DOI: 10.2140/agt.2017.17.3057

Abstract

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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Keywords

knot concordance, pretzel knots

Mathematical Subject Classification 2010

Primary: 57M25

Secondary: 57N70

References

Publication

Received: 1 November 2016

Revised: 15 April 2017

Accepted: 13 June 2017

Published: 19 September 2017

Authors

Allison N Miller
Department of Mathematics University of Texas Austin, TX United States
http://www.ma.utexas.edu/users/amiller/

Volume 17, issue 5 (2017)