Simple ribbon fusions and genera of links

Abstract

Let K be the result of a 1-fusion (band sum) of a knot k and a distant trivial knot in S³. 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.