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I would like to find an appropriate reference for the following statement:

Statement. Let $M$ be a compact Riemannian manifold with non-negative Ricci curvature. Then $\pi_1(M)$ is virtually abelian.

It seems to me that the statement should follow from the article of Cheeger and Gromoll "The spletting theorem for manifolds of non-negative Ricci curvature" http://intlpress.com/JDG/archive/1972/6-1-119.pdf but since it is not stated explicitly in the article I am not 100% sure.

So, what would be a reference?

edited Oct 24 at 12:12

Francesco Polizzi
19k●2●34●55

asked Oct 24 at 11:25

aglearner
3,868●8●24

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Is it not precisely Theorem 3 (pag 126) in the paper by Cheeger and Gromoll? – Francesco Polizzi Oct 24 at 12:11

Francesco, huge thanks! Of course you are right, I overlooked this theorem (shame for me :) ... ). – aglearner Oct 24 at 12:27

ε-δ · Accepted Answer · 2012-10-24 18:12:38Z UTC

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The following paper has more than you want.

Wilking, Burkhard On fundamental groups of manifolds of nonnegative curvature. Differential Geom. Appl. 13 (2000), no. 2, 129–165.

answered Oct 24 at 18:12

ε-δ
1,028●5●16

Fundamental groups of compact manifolds with non-negative Ricci curvature.

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