Mp-small summands increase knot width
Abstract
Scharlemann and Schultens have shown that for any pair of knots K1 and K2, w(K1 # K2) is greater than or equal to maxw(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 the connected sum of mp-small knots and K' any non-trivial knot, w(K # K')>w(K).
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