Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 5, pages 135--144.

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 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.

Keywords. Knot, width, additivity, Haken surfaces

AMS subject classification. Primary: 11Y16, 57M50. Secondary: 57M25.

E-print: arXiv:math.GT/0403326

Submitted to GT on 19 March 2004. (Revised 28 July 2004.) Paper accepted 4 August 2004. Paper published 18 September 2004.

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

Email: mgscharl@math.ucsb.edu, thompson@math.ucdavis.edu

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