Asian Journal of Mathematics
Volume 9 (2005)
On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions
Pages: 545 – 560
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.