We shall describe, without technicalities, the main ideas of an
  alternative approach for the last step in Perelman's proof of
  Thurston's Geometrization Conjecture. This is joint work with
  L. Bessieres, M. Boileau, S. Maillot and J. Porti. Using two
  covering arguments we reduce the problem to Thurston's proof of his
  conjecture for Haken manifolds. One of the arguments makes use of
  Gromov's simplicial volume.