Mp-small summands increase knot width (Q1766290)

The author contributes to results on ``thin position'' and ``knot width'' obtained by \textit{A. Thompson} by \textit{Y. Rieck} and \textit{E. Sedgwick} and by \textit{M. Scharlemann} and \textit{J. Schultens} -- see the paper of the latter authors, [3-manifolds with planar presentations and the width of satelite knots, arXiv: math. GT/0304271] for definitions. The following is proved: If \(K_1\) is an mp-small knot, then for any non-trivial knot \(K_2\), \(w(K_1\sharp K_2)> w(K_1)\). (\(w(k)=\) width of the knot \(K\).) The same is shown for \(K_1\) a connected sum of mp-small knots. The proof is obtained by cleverly piecing together results of the aforesaid authors.