Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Mp-small summands increase knot width

Jacob Hendricks

Algebraic & Geometric Topology 4 (2004) 1041–1044

arXiv: math.GT/0406072

Abstract

Scharlemann and Schultens have shown that for any pair of knots K1 and K2, w(K1#K2) max{w(K1),w(K2)}. 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=1nKi 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