On the additivity of knot width

2004/03/31 by Martin Scharlemann, Abigail Thompson
Mathematics · #math.GT #msc:11Y16 #msc:57M50 #msc:57M25

paper · pdf

published as Geom. Topol. Monogr. 7 (2004) 135-144 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper5.abs.html

arxiv created 2004/09/20 · arxiv updated 2009/12/01

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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