Papers
Topics
Authors
Recent
Search
2000 character limit reached

Revised note on surface-link of trivial components

Published 7 Mar 2025 in math.GT | (2503.05151v1)

Abstract: 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.

Summary

No one has generated a summary of this paper yet.

Paper to Video (Beta)

No one has generated a video about this paper yet.

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Collections

Sign up for free to add this paper to one or more collections.

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.