#### Algebraic and Geometric Topology 4 (2004),
paper no. 44, pages 1041-1044.

## Mp-small summands increase knot width

### Jacob Hendricks

**Abstract**.
Scharlemann and Schultens have shown that for any pair of knots K_1
and K_2, w(K_1 # K_2) >= max{w(K_1),w(K_2)}. Scharlemann and Thompson
have given a scheme for possible examples where equality holds. Using
results of Scharlemann-Schultens, Rieck-Sedgwick and Thompson, it is
shown that for K= #_{i=1}^n K_i a connected sum of mp-small knots and
K' any non-trivial knot, w(K # K')>w(K).
**Keywords**.
Thin position, knot width

**AMS subject classification**.
Primary: 57M25.
Secondary: 57M27.

**DOI:** 10.2140/agt.2004.4.1041

**E-print:** `arXiv:math.GT/0406072`

Submitted: 14 June 2004.
(Revised: 20 August 2004.)
Accepted: 7 September 2004.
Published: 3 November 2004.

Notes on file formats
Jacob Hendricks

Department of Mathematics, University of Arkansas

Fayetteville, AR 72701, USA

Email: jghendr@uark.edu

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