Revised note on surface-link of trivial components
Revised note on surface-link of trivial components
In a previous note, it is claimed that every surface-link consisting of trivial components and having at most one non-sphere component is a ribbon surface-link, but it was false. In this revised note, this claim is replaced by the claim that a surface-link $L$ with trivial components is a ribbon surface-link if and only if the surface-link obtained from $L$ by every fusion is a ribbon surface-link if and only if the surface-link obtained from $L$ by any one fusion is a ribbon surface-link. For any closed oriented disconnected surface ${\mathbf F}$ containing at least two non-sphere components, there is a pair of a ribbon ${\mathbf F}$-link $L$ consisting of trivial components and a non-ribbon ${\mathbf F}$-link $L'$ consisting of trivial components such that the fundamental groups of $L$ and $L'$ are the same group up to meridian-preserving isomorphisms and the pair of the ${\mathbf F}'$-links $K$ and $K'$ obtained from $L$ and $L'$ by every corresponding fusion is a pair of a ribbon surface-link and a non-ribbon surface-link such that the fundamental groups of $K$ and $K'$ are the same group up to meridian-preserving isomorphisms.
Akio Kawauchi
数学
Akio Kawauchi.Revised note on surface-link of trivial components[EB/OL].(2025-03-07)[2025-05-17].https://arxiv.org/abs/2503.05151.点此复制
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