Convergence and collapsing of CAT$(0)$-lattices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929334605840384 |
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| author | Cavallucci, Nicola Sambusetti, Andrea |
| author_facet | Cavallucci, Nicola Sambusetti, Andrea |
| contents | We study the theory of convergence for CAT$(0)$-lattices (that is groups $Γ$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how these action can degenerate to a possibly non-discrete limit action. Finally, we prove a compactness theorem for the class of compact CAT$(0)$-homology orbifolds, and some applications: an isolation result for flat orbispaces and an entropy-pinching theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence and collapsing of CAT$(0)$-lattices Cavallucci, Nicola Sambusetti, Andrea Metric Geometry Differential Geometry Group Theory We study the theory of convergence for CAT$(0)$-lattices (that is groups $Γ$ acting geometrically on proper, geodesically complete CAT$(0)$-spaces) and their quotients (CAT$(0)$-orbispaces). We describe some splitting and collapsing phenomena, explaining precisely how these action can degenerate to a possibly non-discrete limit action. Finally, we prove a compactness theorem for the class of compact CAT$(0)$-homology orbifolds, and some applications: an isolation result for flat orbispaces and an entropy-pinching theorem. |
| title | Convergence and collapsing of CAT$(0)$-lattices |
| topic | Metric Geometry Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2405.01595 |