Communications in Analysis and Geometry

Volume 29 (2021)

Number 2

On the visibility of the +achirality of alternating knots

Pages: 409 – 463

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n2.a5

Authors

Nicola Ermotti (Section de Mathématiques, Université de Genève, Switzerland)

Cam Van Quach Hongler (Section de Mathématiques, Université de Genève, Switzerland)

Claude Weber (Section de Mathématiques, Université de Genève, Switzerland)

Abstract

This article is devoted to the study of prime alternating +achiral knots. In the case of arborescent knots, we prove in +AAA Visibility Theorem 5.1, that the symmetry is visible on a certain projection (not necessarily minimal) and that it is realised by a homeomorphism of order $4$. In the general case (arborescent or not), if the prime alternating knot has no minimal projection on which +achirality is visible, we prove that the order of +achirality is necessarily equal to $4$.

Received 15 March 2015

Accepted 15 August 2018