The warping degree of a knot diagram
Geometric Topology
2009-06-02 v4
Abstract
For an oriented knot diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain the monotone diagram from D in the usual way. We show that d(D) + d(-D) + 1 is less than or equal to the crossing number of D. Moreover the equality holds if and only if D is an alternating diagram.
Keywords
Cite
@article{arxiv.0809.1334,
title = {The warping degree of a knot diagram},
author = {Ayaka Shimizu},
journal= {arXiv preprint arXiv:0809.1334},
year = {2009}
}
Comments
12 pages, 9 figures