Geodesic
The topological sliceness of 3–strand pretzel knots
Miller, Allison1
1 Department of Mathematics, University of Texas, Austin, TX, United States
Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 3057-3079

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2017.17.3057
Classification : 57M25, 57N70
Keywords: knot concordance, pretzel knots

Miller, Allison 1

1 Department of Mathematics, University of Texas, Austin, TX, United States 
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Miller, Allison. The topological sliceness of 3–strand pretzel knots. Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 3057-3079. doi: 10.2140/agt.2017.17.3057

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