📝 SummarXiv

Abstract

It is shown that a surface-link of ribbon surface-knot components is a ribbon surface-link if and only if it is a surface-link producing a ribbon surface-link by surgery along a self-trivial 1-handle system. This corrects an earlier statement. This result makes a corrected proof for the claim that every surface-link of trivial surface-knot components with at most one aspheric component is a ribbon surface-link. For non-ribbon surface-links of trivial components with at least two aspheric components constructed in a previous note, it adds the new property that non-ribbonability continues through surgery along any self-trivial 1-handle system.