GENERALIZED TEICHMÜLLER SPACE OF NON-COMPACT 3-MANIFOLDS AND MOSTOW RIGIDITY

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 spaceT of complete hyperbolic metrics onN with cone singularities along the edges of the tetrahedra. We prove that T is homeomorphic to a Euclidean space and we compute its dimension. By means of examples, we examine if the elements of T are uniquely determined by the angles around the edges of N. 1