Generalized Teichm\"{u}ller space of non-compact 3-manifolds and Mostow rigidity

Charalampos Charitos; Ioannis Papadoperakis

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arXiv · 1007.2346

Generalized Teichm\"{u}ller space of non-compact 3-manifolds and Mostow rigidity

Charalampos Charitos·Ioannis Papadoperakis

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Abstract

Consider a 3$-$dimensional manifold $N$ obtained by gluing a finite number of ideal hyperbolic tetrahedra via isometries along their faces. By varying the isometry type of each tetrahedron but keeping fixed the gluing pattern we define a space $\mathcal{T}$ of complete hyperbolic metrics on $N$ with cone singularities along the edges of the tetrahedra. We prove that $\mathcal{T}$ is homeomorphic to a Euclidean space and we compute its dimension. By means of examples, we examine if the elements of $% \mathcal{T}$ are uniquely determined by the angles around the edges of $N.$

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BibTeX RIS

Charalampos Charitos, Ioannis Papadoperakis. 2010-07-14. Generalized Teichm\"{u}ller space of non-compact 3-manifolds and Mostow rigidity. https://arxiv.org/abs/1007.2346

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