On the additivity of knot width

Details On the additivity of knot width On the additivity of knot width

2004-03-19

arxiv.org/abs/math/0403326v2

Geom. Topol. Monogr. 7 (2004) 135-144

Mathematics

Geometric Topology

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper5.abs.html

Scientific paper

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 S^3, the conjecture is that w(K # K') = w(K) + w(K') - 2.
We give an example of a knot K_1 so that for K_2 any 2-bridge knot, it appears
that w(K_1 # K_2) = w(K_1), contradicting the conjecture.

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