Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link
Abstract
There is a question asking whether a handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link. This question for the case of a trivial surface-link is affirmatively answered. That is, a handle-irreducible summand of every stably trivial surface-link is only a trivial 2-link. By combining this result with an old result of F. Hosowaka and the author that every surface-knot with infinite cyclic fundamental group is a stably trivial surface-knot, it is concluded that every surface-knot with infinite cyclic fundamental group is a trivial (i.e., an unknotted) surface-knot.
Keywords
Cite
@article{arxiv.1804.02654,
title = {Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link},
author = {Akio Kawauchi},
journal= {arXiv preprint arXiv:1804.02654},
year = {2022}
}
Comments
This is the part I on "Ribbonness of a stable-ribbon surface-link". New revision of Section 3 is added as the separated paper "Uniqueness of an orthogonal 2-handle pair on a surface-link"