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

2012-10-24T11:25:47Z

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?

Answer by ε-δ for Fundamental groups of compact manifolds with non-negative Ricci curvature.

2012-10-24T18:12:38Z

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.

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

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

Answer by ε-δ for Fundamental groups of compact manifolds with non-negative Ricci curvature.