Communications in Analysis and Geometry

Volume 27 (2019)

Number 8

A topological characterization of toroidally alternating knots

Pages: 1825 – 1850

DOI: https://dx.doi.org/10.4310/CAG.2019.v27.n8.a6

Author

Seungwon Kim (Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang, South Korea)

Abstract

We extend Howie’s characterization of alternating knots to give a topological characterization of toroidally alternating knots, which were defined by Adams. We provide necessary and sufficient conditions for a knot to be toroidally alternating. We also give a topological characterization of almost-alternating knots which is different from Ito’s recent characterization.

Full Text (PDF format)

Received 13 August 2016

Accepted 2 June 2017

Published 21 January 2020