arXiv Analytics

Sign in

arXiv:2407.10467 [math.GT]AbstractReferencesReviewsResources

A lower bound of the crossing number of composite knots

Ruifeng Qiu, Chao Wang

Published 2024-07-15Version 1

Let $c(K)$ denote the crossing number of a knot $K$ and let $K_1\# K_2$ denote the connected sum of two oriented knots $K_1$ and $K_2$. It is a very old unsolved question that whether $c(K_1\# K_2)=c(K_1)+c(K_2)$. In this paper we show that $c(K_1\# K_2)> (c(K_1)+c(K_2))/16$.

Comments: 46 pages, 45 figures
Categories: math.GT
Subjects: 57M25, 57N10
Related articles: Most relevant | Search more
arXiv:0805.4706 [math.GT] (Published 2008-05-30, updated 2009-08-25)
The crossing number of composite knots
arXiv:math/0110174 [math.GT] (Published 2001-10-17)
Crossing number of links formed by edges of a triangulation
arXiv:math/0110016 [math.GT] (Published 2001-10-01)
On the crossing number of positive knots and braids and braid index criteria of Jones and Morton-Williams-Franks

Links

Toolbox