Inventiones mathematicae

, Volume 126, Issue 1, pp 47–64

The almost cyclicity of the fundamental groups of positively curved manifolds

  • Xiaochun Rong

DOI: 10.1007/s002220050088

Cite this article as:
Rong, X. Invent math (1996) 126: 47. doi:10.1007/s002220050088


 Recall that a pure F-structure is a kind of generalized torus action. The main result asserts that if a compact positively curved manifold Mn admits an invariant pure F-structure such that each orbit has positive dimension, then the fundamental group has a finite cyclic subgroup with index less than wn, a constant depending only on n. As an application, we conclude that for all 0<δ≦1, the fundamental group of a δ-pinched n-manifold either has a cyclic subgroup with index less than wn or has order less than w(n,δ), a constant depending only on n and δ. In particular, this substantially improves the main result in[Ro1].

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Xiaochun Rong
    • 1
  1. 1.Mathematics Department, University of Chicago, Chicago, IL 60637, USA; e-mail: xr@math.uchicago.eduUS