On the $n$-transitivity of the group of equivariant diffeomorphisms
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909259780849664 |
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| author | Kankaanrinta, Marja |
| author_facet | Kankaanrinta, Marja |
| contents | Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. If $M$ is connected and $\dim(M)\geq 2$, the group of diffeomorphisms of $M$, that are isotopic to the identity through a compactly supported isotopy, acts $n$-transitively on $M$, for any $n$. In this paper, we prove a version of the $n$-transitivity result for the group of equivariant diffeomorphisms of $M$. As a corollary we obtain a result concerning diffeomorphisms of the orbit space $M/G$. A special case of the result for orbit spaces gives an $n$-transitivity result for orbifold diffeomorphisms that was earlier proved by F. Pasquotto and T. O. Rot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12510 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the $n$-transitivity of the group of equivariant diffeomorphisms Kankaanrinta, Marja Geometric Topology 57S20 57R18 57S05 Let $G$ be a Lie group and let $M$ be a proper smooth $G$-manifold. If $M$ is connected and $\dim(M)\geq 2$, the group of diffeomorphisms of $M$, that are isotopic to the identity through a compactly supported isotopy, acts $n$-transitively on $M$, for any $n$. In this paper, we prove a version of the $n$-transitivity result for the group of equivariant diffeomorphisms of $M$. As a corollary we obtain a result concerning diffeomorphisms of the orbit space $M/G$. A special case of the result for orbit spaces gives an $n$-transitivity result for orbifold diffeomorphisms that was earlier proved by F. Pasquotto and T. O. Rot. |
| title | On the $n$-transitivity of the group of equivariant diffeomorphisms |
| topic | Geometric Topology 57S20 57R18 57S05 |
| url | https://arxiv.org/abs/2407.12510 |