Partially hyperbolic lattice actions on 2-step nilmanifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910627554918400 |
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| author | Lee, Homin Sandfeldt, Sven |
| author_facet | Lee, Homin Sandfeldt, Sven |
| contents | We prove global rigidity results for actions of higher rank lattices on nilmanifolds containing a partially hyperbolic element. We consider actions of higher rank lattices on tori or on $2-$step nilpotent nilmanifolds, such that the actions contain a partially hyperbolic element with $1-$dimensional center. In this setting we prove, under a technical assumption on the partially hyperbolic element, that any such action must be by affine maps. This extends results by Brown, Rodriguez Hertz, and Wang to certain lattice actions that are not Anosov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Partially hyperbolic lattice actions on 2-step nilmanifolds Lee, Homin Sandfeldt, Sven Dynamical Systems 37C85 (Primary) 37C15, 37D30 (Secondary) We prove global rigidity results for actions of higher rank lattices on nilmanifolds containing a partially hyperbolic element. We consider actions of higher rank lattices on tori or on $2-$step nilpotent nilmanifolds, such that the actions contain a partially hyperbolic element with $1-$dimensional center. In this setting we prove, under a technical assumption on the partially hyperbolic element, that any such action must be by affine maps. This extends results by Brown, Rodriguez Hertz, and Wang to certain lattice actions that are not Anosov. |
| title | Partially hyperbolic lattice actions on 2-step nilmanifolds |
| topic | Dynamical Systems 37C85 (Primary) 37C15, 37D30 (Secondary) |
| url | https://arxiv.org/abs/2410.00784 |