Simple ribbon fusions and genera of links. (English) Zbl 1357.57015

Kishimoto, Kengo; Shibuya, Tetsuo; Tsukamoto, Tatsuya

J. Math. Soc. Japan 68, No. 3, 1033-1045 (2016).

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)

Keywords:

link; fusion; genus