# The crossing number of composite knots

Lackenby, M

2009

## Journal:

JOURNAL OF TOPOLOGY

## Last Updated:

2021-10-19T13:18:52.797+01:00

4

2

## DOI:

10.1112/jtopol/jtp028

747-768

## 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.

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