A characterisation of alternating knot exteriors

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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
Issue number4
Publication statusPublished - 19 May 2017
Externally publishedYes

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