Algebraic & Geometric Topology

The topological sliceness of $3$–strand pretzel knots

Allison Miller

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

knot concordance pretzel knots


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.

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