## Journal of the Mathematical Society of Japan

### 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 $S^3$. 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 68, Number 3 (2016), 1033-1045.

Dates
First available in Project Euclid: 19 July 2016

https://projecteuclid.org/euclid.jmsj/1468956158

Digital Object Identifier
doi:10.2969/jmsj/06831033

Mathematical Reviews number (MathSciNet)
MR3523537

Zentralblatt MATH identifier
1357.57015

Keywords