arXiv Analytics

Sign in

arXiv:0805.4706 [math.GT]AbstractReferencesReviewsResources

The crossing number of composite knots

Marc Lackenby

Published 2008-05-30, updated 2009-08-25Version 2

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.

Comments: 28 pages, 20 figures; final version, to appear in the Journal of Topology
Categories: math.GT
Subjects: 57M25, 57N10
Related articles: Most relevant | Search more
arXiv:2407.10467 [math.GT] (Published 2024-07-15)
A lower bound of the crossing number of composite knots
arXiv:1310.5054 [math.GT] (Published 2013-10-18, updated 2013-10-22)
On the degeneration of tunnel numbers under connected sum
arXiv:1503.01188 [math.GT] (Published 2015-03-04)
A criterion for the Legendrian simplicity of the connected sum

Links

Toolbox