A characterisation of alternating knot exteriors

Research output: Contribution to journalArticleResearchpeer-review

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.

Original languageEnglish
Pages (from-to)2353-2371
Number of pages19
JournalGeometry and Topology
Volume21
Issue number4
DOIs
Publication statusPublished - 19 May 2017
Externally publishedYes

Cite this

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A characterisation of alternating knot exteriors. / Howie, Joshua A.

In: Geometry and Topology, Vol. 21, No. 4, 19.05.2017, p. 2353-2371.

Research output: Contribution to journalArticleResearchpeer-review

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