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arXiv · 1511.04945

A characterisation of alternating knot exteriors

Joshua Howie
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Abstract

We give a topological characterisation of alternating knot exteriors based on the presence of special spanning surfaces. This shows that 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 prime and alternating given a triangulation of its exterior as input.

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Joshua Howie. 2015-11-16. A characterisation of alternating knot exteriors. https://doi.org/10.2140/gt.2017.21.2353

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