Mp-small summands increase knot width

Hendricks, Jacob

doi:10.2140/agt.2004.4.1041

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Mp-small summands increase knot width

Jacob Hendricks

Algebraic & Geometric Topology 4 (2004) 1041–1044

DOI: 10.2140/agt.2004.4.1041

arXiv: math.GT/0406072

Abstract

Scharlemann and Schultens have shown that for any pair of knots $K_{1}$ and $K_{2}$ , $w (K_{1} # K_{2}) \geq m a x {w (K_{1}), w (K_{2})}$ . 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

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

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Publication

Received: 14 June 2004

Revised: 20 August 2004

Accepted: 7 September 2004

Published: 3 November 2004

Authors

Jacob Hendricks
Department of Mathematics University of Arkansas Fayetteville AR 72701 USA

Volume 4, issue 2 (2004)