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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