Effect of a crossing change on crossing number
Geometric Topology
2011-03-25 v1
Abstract
The purpose of this article is to give a preliminary clarification on the relation between crossing number and crossing change. With a main focus on the span of X polynomial, we prove that, as our theorem claims, the crossing number of the link after crossing change can be estimated when certain conditions are met. At the end of the article, we give an example to demonstrate a special case for the theorem and a counterexample to explain that the theorem cannot be applied if the obtained link is not alternating.
Cite
@article{arxiv.1103.4695,
title = {Effect of a crossing change on crossing number},
author = {Longting Wu and Shuting Shao and Shan Liu and Fengchun Lei},
journal= {arXiv preprint arXiv:1103.4695},
year = {2011}
}
Comments
11 pages, 12 figures