Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry

Abstract

Let M be an n-manifold of positive sectional curvature ≥ 1. In this paper, we show that if the Riemannian universal covering has volume at least v > 0, then the fundamental group π₁(M) has a cyclic subgroup of index bounded above by a constant depending only on n and v.

Keywords

Positive sectional curvature / fundamental groups / the c(n)-cyclic conjecture