Mp-small summands increase knot width
arXiv:math/0406072 · doi:10.2140/agt.2004.4.1041
Abstract
Scharlemann and Schultens have shown that for any pair of knots K_1 and K_2, w(K_1 # K_2) is greater than or equal to 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 the connected sum of mp-small knots and K' any non-trivial knot, w(K # K')>w(K).
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-44.abs.html