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.
Citation
Joshua Howie. "A characterisation of alternating knot exteriors." Geom. Topol. 21 (4) 2353 - 2371, 2017. https://doi.org/10.2140/gt.2017.21.2353
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