📝 SummarXiv

Abstract

It is shown that a boundary surface-link in the 4-sphere is a ribbon surface-link if the surface-knot obtained from it by surgery along a pairwise nontrivial 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-handle is a non-ribbon surface-knot. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative.