1.3. Gromov’s theorem 23 Proposition 1.3.2. Let M be a compact Riemannian manifold of nonneg- ative Ricci curvature. Then the fundamental group π1(M) of M is virtually nilpotent. We will discuss this result and some related results (such as a relaxation of the nonnegative curvature hypothesis to an almost nonnegative curvature hypothesis) in Section 10. We also remark that the above proposition can also be proven (with stronger conclusions) by more geometric means, but there are some results of the above type which currently have no known proof that does not employ some version of Gromov’s theorem at some point.
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