TL;DR
The paper provides a revised proof relating boundary surface-links in 4-sphere to ribbon surface-links via handle surgery, confirming Cochran's conjecture and constructing non-ribbon surface links.
Contribution
It offers a new proof connecting boundary surface-links and ribbon surface-links, confirming Cochran's conjecture and constructing examples of non-ribbon links.
Findings
Boundary surface-link is ribbon if surgery yields a ribbon surface-link.
Corollary confirms non-ribbon surface-knots from anti-parallel links.
Infinite family of non-ribbon surface links with trivial components constructed.
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.
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