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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A characterisation of alternating knot exteriors

Joshua A Howie

Geometry & Topology 21 (2017) 2353–2371
Abstract

We give a topological characterisation of alternating knot exteriors based on the presence of special spanning surfaces. This shows that being alternating is a topological property of the knot exterior and not just a property of diagrams, answering an old question of Fox. We also give a characterisation of alternating link exteriors which have marked meridians. We then describe a normal surface algorithm which can decide if a knot is alternating given a triangulation of its exterior as input.

Keywords
alternating knot, alternating link, spanning surface, normal surface algorithm
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 5 February 2016
Accepted: 19 September 2016
Published: 19 May 2017
Proposed: Cameron Gordon
Seconded: Ciprian Manolescu, András I. Stipsicz
Authors
Joshua A Howie
School of Mathematics and Statistics
University of Melbourne
Melbourne VIC 3010
Australia