On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions

Abstract

In this paper, we study the fundamental groups of closed manifolds of positive sectional curvature which admit compatible local isometric torus $T^k$-actions. We explore relations between basic properties of an isometric $T^k$-action and the structure of the fundamental group of $M$. Using these relations, we prove several results on the fundamental groups.