2011/03/24 by Longting Wu, Shuting Shao, Wu, Longting +5
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1103.4695
11 pages, 12 figures
arxiv created 2011/03/24 · arxiv updated 2011/03/25
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.