Free Group Actions from the Viewpoint of Dynamical Systems
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2011
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| _version_ | 1866912783575023616 |
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| author | Wagner, Stefan |
| author_facet | Wagner, Stefan |
| contents | In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we provide conditions including the existence of "sufficiently many" representations of the transformation group which ensure that the corresponding action of that group on the spectrum of the algebra is free. In particular, the case of compact abelian groups is discussed very carefully. We further present an application to the structure theory of C*-algebras and an application to the noncommutative geometry of principal bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1111_5562 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | Free Group Actions from the Viewpoint of Dynamical Systems Wagner, Stefan Differential Geometry 37B05, 55R10, 46L87 In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we provide conditions including the existence of "sufficiently many" representations of the transformation group which ensure that the corresponding action of that group on the spectrum of the algebra is free. In particular, the case of compact abelian groups is discussed very carefully. We further present an application to the structure theory of C*-algebras and an application to the noncommutative geometry of principal bundles. |
| title | Free Group Actions from the Viewpoint of Dynamical Systems |
| topic | Differential Geometry 37B05, 55R10, 46L87 |
| url | https://arxiv.org/abs/1111.5562 |