Analysis shows conditions for boundary surface-links to be ribbon surface-links, indicating new insights on knots.
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 fusion 1-handleis a non-ribbon surface-knot. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative.
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Akio Kawauchi (2025) studied this question.
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