Weak collapsing and geometrisation of aspherical 3-manifolds

Details Weak collapsing and geometrisation of aspherical 3-manifolds Weak collapsing and geometrisation of aspherical 3-manifolds

2007-06-14

arxiv.org/abs/0706.2065v2

Mathematics

Geometric Topology

Improved version in English

Scientific paper

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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