Algebraic & Geometric Topology

The topological sliceness of $3$–strand pretzel knots

Allison Miller

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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.

Article information

Source
Algebr. Geom. Topol., Volume 17, Number 5 (2017), 3057-3079.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841492

Digital Object Identifier
doi:10.2140/agt.2017.17.3057

Mathematical Reviews number (MathSciNet)
MR3704252

Zentralblatt MATH identifier
1376.57010

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N70: Cobordism and concordance

Keywords
knot concordance pretzel knots

Citation

Miller, Allison. The topological sliceness of $3$–strand pretzel knots. Algebr. Geom. Topol. 17 (2017), no. 5, 3057--3079. doi:10.2140/agt.2017.17.3057. https://projecteuclid.org/euclid.agt/1510841492


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