#### 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
##### 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
Primary: 57M25
Secondary: 57N70