#### 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

and

Mathematics Department, University of
California

Davis, CA 95616, USA

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

GTM home page

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