A characterisation of alternating knot exteriors

Howie, Joshua

doi:10.2140/gt.2017.21.2353

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A characterisation of alternating knot exteriors

Joshua A Howie

Geometry & Topology 21 (2017) 2353–2371

DOI: 10.2140/gt.2017.21.2353

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

Volume 21, issue 4 (2017)