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Boundedness of diffeomorphism groups of manifold pairs -- Circle case -- ...
| العنوان: | Boundedness of diffeomorphism groups of manifold pairs -- Circle case -- ... |
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| المؤلفون: | Fukui, Kazuhiko, Yagasaki, Tatsuhiko |
| بيانات النشر: | arXiv |
| سنة النشر: | 2025 |
| المجموعة: | DataCite Metadata Store (German National Library of Science and Technology) |
| مصطلحات موضوعية: | Geometric Topology math.GT, Group Theory math.GR, FOS: Mathematics, 57R50, 57R52, 37C05 |
| الوصف: | In this paper we study boundedness of conjugation invariant norms on diffeomorphism groups of manifold pairs. For the diffeomorphism group ${\mathcal D} \equiv {\rm Diff}(M,N)_0$ of a closed manifold pair $(M, N)$ with $\dim N \geq 1$, first we clarify the relation among the fragmentation norm, the conjugation generated norm, the commutator length $cl$ and the commutator length with support in balls $clb$ and show that ${\mathcal D}$ is weakly simple relative to a union of some normal subgroups of ${\mathcal D}$. For the boundedness of these norms, this paper focuses on the case where $N$ is a union of $m$ circles. In this case, the rotation angle on $N$ induces a quasimorphism $ν: {\rm Isot}(M, N)_0 \to {\Bbb R}^m$, which determines a subgroup $A$ of ${\Bbb Z}^m$ and a function $\widehatν : {\mathcal D} \to {\Bbb R}^m/A$. If ${\rm rank}\,A = m$, these data leads to an upper bound of $clb$ on ${\mathcal D}$ modulo the normal subgroup ${\mathcal G} \cong {\rm Diff}_c(M - N)_0$. Then, some upper bounds of $cl$ ... : 34 pages ... |
| نوع الوثيقة: | report article in journal/newspaper |
| اللغة: | unknown |
| DOI: | 10.48550/arxiv.2501.11363 |
| الاتاحة: | https://dx.doi.org/10.48550/arxiv.2501.11363 https://arxiv.org/abs/2501.11363 |
| Rights: | Creative Commons Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0/legalcode ; cc-by-4.0 |
| رقم الانضمام: | edsbas.D806DD88 |
| قاعدة البيانات: | BASE |
| DOI: | 10.48550/arxiv.2501.11363 |
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