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On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions

Xiaochun Rong
Source: Asian J. Math. Volume 9, Number 4 (2005), 545-560.

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.

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