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

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