Generalized Teichm "uller space of non-compact 3-manifolds and Mostow\n rigidity

2010/07/14 by Charalampos Charitos, Charitos, Charalampos, Ioannis Papadoperakis +1
Computer Science · Mathematics · #57M50 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1007.2346

openalex publication_date 2010/07/14 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Consider a 3-dimensional manifold N obtained by gluing a finite number of\nideal hyperbolic tetrahedra via isometries along their faces. By varying the\nisometry type of each tetrahedron but keeping fixed the gluing pattern we\ndefine a space \T of complete hyperbolic metrics on N with cone\nsingularities along the edges of the tetrahedra. We prove that \T is\nhomeomorphic to a Euclidean space and we compute its dimension. By means of\nexamples, we examine if the elements of % \T are uniquely determined\nby the angles around the edges of N.\n

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