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Simple ribbon fusions and genera of links. (English) Zbl 1357.57015
Summary: Let $$K$$ be the result of a 1-fusion (band sum) of a knot $$k$$ and a distant trivial knot in $$S^3$$. From results of D. Gabai and of M. G. Scharlemann, we know that the genus of $$K$$ is at least that of $$k$$ and that equality holds if and only if the band sum is, in fact, a connected sum (in which case $$K$$ is ambient isotopic to $$k$$). In this paper, we consider a generalization of this result to an $$m$$-fusion of a link and a distant trivial link with $$m$$-components.

##### MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010)