The deformation space of non-orientable hyperbolic 3-manifolds
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917622213246976 |
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| author | Batalla, Juan Luis Durán Porti, Joan |
| author_facet | Batalla, Juan Luis Durán Porti, Joan |
| contents | We consider non-orientable hyperbolic 3-manifolds of finite volume $M^3$. When $M^3$ has an ideal triangulation $Δ$, we compute the deformation space of the pair $(M^3, Δ)$ (its Neumann Zagier parameter space). We also determine the variety of representations of $π_1(M^3)$ in $\mathrm{Isom}(\mathbb{H}^3)$ in a neighborhood of the holonomy. As a consequence, when some ends are non-orientable, there are deformations from the variety of representations that cannot be realized as deformations of the pair $(M^3, Δ)$. We also discuss the metric completion of these structures and we illustrate the results on the Gieseking manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_01027 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The deformation space of non-orientable hyperbolic 3-manifolds Batalla, Juan Luis Durán Porti, Joan Geometric Topology 57K32 We consider non-orientable hyperbolic 3-manifolds of finite volume $M^3$. When $M^3$ has an ideal triangulation $Δ$, we compute the deformation space of the pair $(M^3, Δ)$ (its Neumann Zagier parameter space). We also determine the variety of representations of $π_1(M^3)$ in $\mathrm{Isom}(\mathbb{H}^3)$ in a neighborhood of the holonomy. As a consequence, when some ends are non-orientable, there are deformations from the variety of representations that cannot be realized as deformations of the pair $(M^3, Δ)$. We also discuss the metric completion of these structures and we illustrate the results on the Gieseking manifold. |
| title | The deformation space of non-orientable hyperbolic 3-manifolds |
| topic | Geometric Topology 57K32 |
| url | https://arxiv.org/abs/2011.01027 |