2012/01/13 by Alexandre Paiva Barreto, Barreto, Alexandre Paiva
Mathematics · Physics and Astronomy · #55m20 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1201.2923
openalex publication_date 2012/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work is devoted to the study of deformations of hyperbolic cone structures under the assumption that the lengths of the singularity remain uniformly bounded over the deformation. Given a sequence (Mi%, pi) of pointed hyperbolic cone-manifolds with topological type (M,Σ) , where M is a closed, orientable and irreducible 3-manifold and Σ an embedded link in M. If the sequence Mi collapses and assuming that the lengths of the singularity remain uniformly bounded, we prove that M is either a Seifert fibered or a Sol manifold. We apply this result to a question stated by Thurston and to the study of convergent sequences of holonomies.