TY - JOUR
T1 - Collapsing irreducible 3-manifolds with nontrivial fundamental group
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
SN - 0020-9910
VL - 179
SP - 435
EP - 460
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 2
ER -