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Prime amphicheiral knots with free period 2

Part of: Low-dimensional topology

Published online by Cambridge University Press:  30 August 2019

Luisa Paoluzzi  and
Makoto Sakuma
Luisa Paoluzzi
Affiliation:
Aix-Marseille Univ, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France (luisa.paoluzzi@univ-amu.fr)
Makoto Sakuma
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan (sakuma@hiroshima-u.ac.jp)
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Abstract

We construct prime amphicheiral knots that have free period 2. This settles an open question raised by the second-named author, who proved that amphicheiral hyperbolic knots cannot admit free periods and that prime amphicheiral knots cannot admit free periods of order > 2.

Keywords

prime knotamphicheiral knotfree periodsymmetry

MSC classification

Primary: 57M25: Knots and links in $S^3$
Secondary: 57M50: Geometric structures on low-dimensional manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 105 - 138
Copyright
Copyright © Edinburgh Mathematical Society 2019

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