Inventiones mathematicae

, 179:435

Collapsing irreducible 3-manifolds with nontrivial fundamental group

  • L. Bessières
  • G. Besson
  • M. Boileau
  • S. Maillot
  • J. Porti
Article

DOI: 10.1007/s00222-009-0222-6

Cite this article as:
Bessières, L., Besson, G., Boileau, M. et al. Invent. math. (2010) 179: 435. doi:10.1007/s00222-009-0222-6

Abstract

Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman’s proof of Thurston’s Geometrisation Conjecture.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • L. Bessières
    • 1
  • G. Besson
    • 1
  • M. Boileau
    • 2
  • S. Maillot
    • 3
  • J. Porti
    • 4
  1. 1.Institut Fourier, Université Joseph Fourier (Grenoble I)UMR 5582 CNRS-UJFSaint-Martin-d’HèresFrance
  2. 2.Institut Mathématique de Toulouse, UMR 5219 CNRS-UPSUniversité Paul SabatierToulouse Cedex 9France
  3. 3.Institut de Mathématiques et de Modélisation de Montpellier, Université de MontpellierUMR 5149 CNRSMontpellier Cedex 5France
  4. 4.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain