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.

Notes on file formats

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


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