Volume 7 (2004)

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On the additivity of knot width

Martin Scharlemann and Abigail Thompson

Geometry & Topology Monographs 7 (2004) 135–144

DOI: 10.2140/gtm.2004.7.135

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)∈2N denote the width of a knot K⊂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.

Keywords

knot, width, additivity, Haken surfaces

Mathematical Subject Classification

Primary: 11Y16, 57M50

Secondary: 57M25

References
Publication

Received: 19 March 2004
Revised: 28 July 2004
Accepted: 4 August 2004
Published: 18 September 2004

Authors
Martin Scharlemann
Mathematics Department
University of California
Santa Barbara CA 93106
USA
Abigail Thompson
Mathematics Department
University of California
Davis CA 95616
USA