The crossing number of composite knots
Geometric Topology
2014-02-26 v2
Abstract
It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least (c(K) + c(K'))/152.
Cite
@article{arxiv.0805.4706,
title = {The crossing number of composite knots},
author = {Marc Lackenby},
journal= {arXiv preprint arXiv:0805.4706},
year = {2014}
}
Comments
28 pages, 20 figures; final version, to appear in the Journal of Topology