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2017 The topological sliceness of $3$–strand pretzel knots
Allison Miller
Algebr. Geom. Topol. 17(5): 3057-3079 (2017). 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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Allison Miller. "The topological sliceness of $3$–strand pretzel knots." Algebr. Geom. Topol. 17 (5) 3057 - 3079, 2017. https://doi.org/10.2140/agt.2017.17.3057

Information

Received: 1 November 2016; Revised: 15 April 2017; Accepted: 13 June 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1376.57010
MathSciNet: MR3704252
Digital Object Identifier: 10.2140/agt.2017.17.3057

Subjects:
Primary: 57M25
Secondary: 57N70

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 5 • 2017
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