Fundamental Groups of Manifolds of Positive Sectional Curvature and Bounded Covering Geometry (Journal of Mathematical Study, 2024)
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 $v > 0,$ thenthe fundamental group $π_1(M)$ has a cyclic subgroup of index bounded above by aconstant depending only on $n$ and $v.$