Abstract
Quasi-ribbon .surface-links are introduced as a generalization of the concept of ribbon surface -links: surface-links that are transformed into ribbon surface-links (without changing the components) by surgery along a locally standard self (1, 2)-handle pair system. For every disconnected closed oriented surface F with at most one aspheric component, every F-link of trivial components is a quasi-ribbon surface-link. For every disconnected closed oriented surface F, there are non-ribbon quasi-ribbon F-links of trivial components. For every closed oriented surface F with at least two aspheric components, there are non-quasi-ribbon F-links of trivial components.
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