Actions of large finite groups on manifolds
In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of $G$ of index bounded above by a number depending only on $X$....
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repository: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/217220 |
| Online Access: | https://hdl.handle.net/2445/217220 |
| Access Level: | Open access |
| Keyword: | Varietats (Matemàtica) Grups de transformacions Manifolds (Mathematics) Transformation groups |
| Summary: | In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of $G$ of index bounded above by a number depending only on $X$. Some of these results refer to the algebraic structure of the group, such as being abelian, or nilpotent, or admitting a generating subset of controlled size; other results refer to the geometry of the action, e.g. to the existence of fixed points, to the collection of stabilizer subgroups, or to the action on cohomology. |
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