## Asian Journal of Mathematics

### On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions

Xiaochun Rong

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 3 May 2006

https://projecteuclid.org/euclid.ajm/1146673653

Mathematical Reviews number (MathSciNet)
MR2216245

Zentralblatt MATH identifier
1100.53037

#### Citation

Rong, Xiaochun. On Fundamental Groups of Positively Curved Manifolds with Local Torus Actions. Asian J. Math. 9 (2005), no. 4, 545--560. https://projecteuclid.org/euclid.ajm/1146673653