The almost alternating diagrams of the trivial knot
Geometric Topology
2014-02-26 v2
Abstract
Bankwitz characterized an alternating diagram representing the trivial knot. A non-alternating diagram is called almost alternating if one crossing change makes the diagram alternating. We characterize an almost alternaing diagram representing the trivial knot. As a corollary we determine an unknotting number one alternating knot with a property that the unknotting operation can be done on its alternating diagram.
Cite
@article{arxiv.math/0605018,
title = {The almost alternating diagrams of the trivial knot},
author = {Tatsuya Tsukamoto},
journal= {arXiv preprint arXiv:math/0605018},
year = {2014}
}
Comments
29 pages, 18 figures