On Nielsen realization and manifold models for classifying spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917575634452480 |
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| author | Davis, James F. Lueck, Wolfgang |
| author_facet | Davis, James F. Lueck, Wolfgang |
| contents | We consider the problem of whether, for a given virtually torsionfree discrete group $Γ$, there exists a cocompact proper topological $Γ$-manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. This problem is related to Nielsen Realization. We will make the assumption that the expected manifold model has a zero-dimensional singular set. Then we solve the problem in the case, for instance, that $Γ$ contains a normal torsionfree subgroup $π$ such that $π$ is hyperbolic and $π$ is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and $Γ/π$ is a finite cyclic group of odd order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15765 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Nielsen realization and manifold models for classifying spaces Davis, James F. Lueck, Wolfgang Geometric Topology 57N99 (Primary), 55R35, 18F25 (Secondary We consider the problem of whether, for a given virtually torsionfree discrete group $Γ$, there exists a cocompact proper topological $Γ$-manifold, which is equivariantly homotopy equivalent to the classifying space for proper actions. This problem is related to Nielsen Realization. We will make the assumption that the expected manifold model has a zero-dimensional singular set. Then we solve the problem in the case, for instance, that $Γ$ contains a normal torsionfree subgroup $π$ such that $π$ is hyperbolic and $π$ is the fundamental group of an aspherical closed manifold of dimension greater or equal to five and $Γ/π$ is a finite cyclic group of odd order. |
| title | On Nielsen realization and manifold models for classifying spaces |
| topic | Geometric Topology 57N99 (Primary), 55R35, 18F25 (Secondary |
| url | https://arxiv.org/abs/2303.15765 |