A characterisation of alternating knot exteriors
Geometric Topology
2017-06-14 v1
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.
Keywords
Cite
@article{arxiv.1511.04945,
title = {A characterisation of alternating knot exteriors},
author = {Joshua Howie},
journal= {arXiv preprint arXiv:1511.04945},
year = {2017}
}
Comments
23 pages, 7 figures