Ribbonness of a Stable-Ribbon Surface-Link, II: General Case

Akio Kawauchi ()
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Akio Kawauchi: Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

Mathematics, 2025, vol. 13, issue 3, 1-11

Abstract: It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are given. One observation is that a connected sum of two surface-links is a ribbon surface-link if and only if both the connected summands are ribbon surface-links. The other observation is a characterization of when a surface-link consisting of ribbon surface-knot components becomes a ribbon surface-link.

Keywords: ribbon surface-link; stable-ribbon surface-link; trivial surface-link; connected sum; O2-handle pair; uniqueness; SUPH system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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