, Volume 126, Issue 1, pp 47-64

The almost cyclicity of the fundamental groups of positively curved manifolds

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Abstract.

 Recall that a pure F-structure is a kind of generalized torus action. The main result asserts that if a compact positively curved manifold M n 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 w n , 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 w n 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].

Oblatum 1-IX-1995 & 26-I-1996