English

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