Reference for proof of Rigid Topological Theorem

Question

Where can I find the proof of the following theorem:

Let $M$ be a compact manifold such that $K\geq 0$. Then there is an exact sequence $$0\to \Phi \to \pi_1(M) \to B\to 0$$ where $\Phi$ is a finite group and $\bf B$ is a crystallographic group on $\Bbb R^k$ for some $k\leq \dim M$.

I would be greatly appreciate if someone provide link of a book or paper for proof and similar theorems?

Answer 1

It is in

J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature,Ann. of Math. 96 (1972) 413–443.

Wilking proved a generalization of this result to manifolds with $Ric\ge 0$ in

On fundamental groups of manifolds of nonnegative curvature, Differential Geometry and its Applications, 13 (2000) 129–165