Collapsing irreducible 3-manifolds with nontrivial fundamental group

L. Bessières; G. Besson; M. Boileau; S. Maillot; J. Porti

doi:10.1007/s00222-009-0222-6

Collapsing irreducible 3-manifolds with nontrivial fundamental group

L. Bessières, G. Besson, M. Boileau, S. Maillot, J. Porti

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

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. © Springer-Verlag 2009.

Original language	English
Pages (from-to)	435-460
Journal	Inventiones Mathematicae
Volume	179
Issue number	2
DOIs	https://doi.org/10.1007/s00222-009-0222-6
Publication status	Published - 1 Dec 2009

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title = "Collapsing irreducible 3-manifolds with nontrivial fundamental group",

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. {\textcopyright} Springer-Verlag 2009.",

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AU - Bessières, L.

AU - Besson, G.

AU - Boileau, M.

AU - Maillot, S.

AU - Porti, J.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - 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. © Springer-Verlag 2009.

AB - 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. © Springer-Verlag 2009.

U2 - 10.1007/s00222-009-0222-6

DO - 10.1007/s00222-009-0222-6

M3 - Article

VL - 179

SP - 435

EP - 460

IS - 2

ER -

Collapsing irreducible 3-manifolds with nontrivial fundamental group

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