On constraints for knots to admit chirally cosmetic surgeries and their calculations

We discuss various constraints for knots in $S^{3}$ to admit chirally cosmetic surgeries, derived from invariants of 3-manifolds, such as, the quantum $SO (3)$ -invariant, the rank of the Heegaard Floer homology, and finite-type invariants. We apply them to show that a large portion (roughly 75%) of knots which are neither amphicheiral nor $(2, p)$ -torus knots with less than or equal to 10 crossings admits no chirally cosmetic surgeries.

Dedicated to Professor Kimihiko Motegi on his sixtieth birthday

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Keywords

chirally cosmetic surgery

Mathematical Subject Classification

Primary: 57K10, 57K16, 57K18, 57K31

Milestones

Received: 7 April 2022

Revised: 14 July 2022

Accepted: 24 July 2022

Published: 3 March 2023

Authors

Kazuhiro Ichihara
Department of Mathematics College of Humanities and Sciences Nihon University Tokyo Japan

Tetsuya Ito
Department of Mathematics Kyoto University Kyoto Japan

Toshio Saito
Department of Mathematics Joetsu University of Education Joetsu Japan

Vol. 321, No. 1, 2022

Kazuhiro Ichihara, Tetsuya Ito and Toshio Saito

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors