Convex co-compact representations of 3-manifold groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866911798906585088 |
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| author | Islam, Mitul Zimmer, Andrew |
| author_facet | Islam, Mitul Zimmer, Andrew |
| contents | A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean $\times$ Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_05191 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Convex co-compact representations of 3-manifold groups Islam, Mitul Zimmer, Andrew Geometric Topology Differential Geometry 53A20, 53A35, 20F67, 57M50, 20H10 A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We prove that the fundamental group of a closed irreducible orientable 3-manifold can admit such a representation only when the manifold is geometric (with Euclidean, Hyperbolic, or Euclidean $\times$ Hyperbolic geometry) or when every component in the geometric decomposition is hyperbolic. In each case, we describe the structure of such examples. |
| title | Convex co-compact representations of 3-manifold groups |
| topic | Geometric Topology Differential Geometry 53A20, 53A35, 20F67, 57M50, 20H10 |
| url | https://arxiv.org/abs/2009.05191 |