Ribbonness on boundary surface-link, revised

Abstract

A revised proof of the author's earlier result is given. It is shown that a boundary surface-link in the 4-sphere is a ribbon surface-link if the surface-link obtained from it by surgery along a pairwise nontrivial fusion 1-handle system is a ribbon surface-link. As a corollary, the surface-knot obtained from the anti-parallel surface-link of a non-ribbon surface-knot by surgery along a nontrivial or trivial fusion 1-handle is a non-ribbon or trivial surface-knot, respectively. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative. An application is made to construct an infinite family of non-ribbon surface links consisting of trivial components with at most one aspheric component.