Weak collapsing and geometrisation of aspherical 3-manifolds
Geometric Topology
2008-01-28 v2
Abstract
Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic and has a sufficiently small volume, then M is Seifert fibred or contains an incompressible torus. This result gives an alternative approach for the last step in Perelman's proof of the Geometrisation Conjecture for aspherical 3-manifolds.
Cite
@article{arxiv.0706.2065,
title = {Weak collapsing and geometrisation of aspherical 3-manifolds},
author = {Laurent Bessières and Gérard Besson and Michel Boileau and Sylvain Maillot and Joan Porti},
journal= {arXiv preprint arXiv:0706.2065},
year = {2008}
}