Locally Collapsed 3-Manifolds
classification
🧮 math.DG
math.GT
keywords
collapsedlocallymanifoldboundcompactconjecturecurvaturedimensional
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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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