3-manifolds with nonnegative Ricci curvature

preprint2012arXivOpen access

Abstract

For a noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to R3\mathbb{R}^3 or the universal cover splits. As a corollary, it confirms a conjecture of Milnor in dimension 3.

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