Unknotting genus one knots
Geometric Topology
2009-05-15 v3
Abstract
For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.
Keywords
Cite
@article{arxiv.0809.4142,
title = {Unknotting genus one knots},
author = {Alexander Coward and Marc Lackenby},
journal= {arXiv preprint arXiv:0809.4142},
year = {2009}
}
Comments
17 pages, 11 figures; v2 corrects an error in Section 4; v3 is the final version. To appear in Commentarii Mathematici Helvetici