Locally Collapsed 3-Manifolds

2010/05/27 by Bruce Kleiner, John Lott, Kleiner, Bruce +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT

paper · pdf · doi:10.48550/arxiv.1005.5106

Final version

arxiv created 2014/06/04 · arxiv updated 2014/06/05

Abstract

We prove that a 3-dimensional compact Riemannian manifold which is locally collapsed, with respect to a lower curvature bound, is a graph manifold. This theorem was stated by Perelman and was used in his proof of the geometrization conjecture.

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