Communications in Analysis and Geometry
Volume 27 (2019)
A topological characterization of toroidally alternating knots
Pages: 1825 – 1850
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.
Received 13 August 2016
Accepted 2 June 2017
Published 21 January 2020