The crossing number of composite knots

Details The crossing number of composite knots The crossing number of composite knots

2008-05-30

arxiv.org/abs/0805.4706v2

Mathematics

Geometric Topology

28 pages, 20 figures; final version, to appear in the Journal of Topology

Scientific paper

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.

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