A note on the fundamental groups of manifolds with almost nonnegative curvature

Yun, Gabjin

doi:10.1090/S0002-9939-97-03756-8

A note on the fundamental groups of manifolds with almost nonnegative curvature
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Proc. Amer. Math. Soc. 125 (1997), 1517-1522 Request permission

Abstract:

We show that given $n$ and $D, v >0$, there exists a positive number $\epsilon = \epsilon (n,D,v)> 0$ such that if a closed $n$-manifold $M$ satisfies $Ric(M) \ge -\epsilon , diam(M) \le D$ and $vol(M) \ge v$, then $\pi _{1}(M)$ is almost abelian.

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