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Mp-small summands increase knot width

Jacob Hendricks
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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).

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Jacob Hendricks. 2004-06-03. Mp-small summands increase knot width. https://doi.org/10.2140/agt.2004.4.1041

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