Weak collapsing and geometrisation of aspherical 3-manifolds

Laurent Bessières; Gérard Besson; Michel Boileau; Sylvain Maillot; Joan Porti

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arXiv · 0706.2065

Weak collapsing and geometrisation of aspherical 3-manifolds

Laurent Bessières·Gérard Besson·Michel Boileau·Sylvain Maillot·Joan Porti

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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.

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Laurent Bessières, Gérard Besson, Michel Boileau, Sylvain Maillot, Joan Porti. 2008-01-28. Weak collapsing and geometrisation of aspherical 3-manifolds. https://arxiv.org/abs/0706.2065

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