On the additivity of knot width
Martin Scharlemann, Abigail Thompson
Abstract
It has been conjectured that the geometric invariant of knots in 3-space called the width is nearly additive. That is, letting w(K) in N denote the width of a knot K in S3, the conjecture is that w(K # K') = w(K) + w(K') - 2. We give an example of a knot K1 so that for K2 any 2-bridge knot, it appears that w(K1 # K2) = w(K1), contradicting the conjecture.
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