Asian Journal of Mathematics

Volume 9 (2005)

Number 4

On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions

Pages: 545 – 560



Xiaochun Rong


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.

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