On the fundamental groups of manifolds of positive sectional curvature

Abstract

Let $M$ be an $n$-manifold with sectional curvature $0 < \delta \le K \le 1$. The main result asserts that the fundamental group of $M$ has a finite normal cyclic subgroup with index less than $w(n,\delta) < \infty$, a constant depending on $n$ and $\delta$.