Nil 3-manifolds and cusps of complex hyperbolic surfaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915036201484288 |
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| author | Paupert, Julien Sell, Connor |
| author_facet | Paupert, Julien Sell, Connor |
| contents | McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of cusped, arithmetic, complex hyperbolic 2-manifolds admit cusps with cross-section homeomorphic to a given compact Nil 3-manifold. In particular, there are some Nil 3-manifolds which occur as cusps in every such commensurability class, and some which only occur in a single commensurability class. We also show that every compact Nil 3-manifold occurs as the cusp cross-section of some non-arithmetic complex hyperbolic 2-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nil 3-manifolds and cusps of complex hyperbolic surfaces Paupert, Julien Sell, Connor Geometric Topology Differential Geometry Group Theory McReynolds showed that every compact Nil 3-manifold occurs as the cusp cross-section of some arithmetic complex hyperbolic 2-manifold. We classify which commensurability classes of cusped, arithmetic, complex hyperbolic 2-manifolds admit cusps with cross-section homeomorphic to a given compact Nil 3-manifold. In particular, there are some Nil 3-manifolds which occur as cusps in every such commensurability class, and some which only occur in a single commensurability class. We also show that every compact Nil 3-manifold occurs as the cusp cross-section of some non-arithmetic complex hyperbolic 2-manifold. |
| title | Nil 3-manifolds and cusps of complex hyperbolic surfaces |
| topic | Geometric Topology Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2411.15345 |