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].
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Oblatum 1-IX-1995 & 26-I-1996
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Rong, X. The almost cyclicity of the fundamental groups of positively curved manifolds. Invent math 126, 47–64 (1996). https://doi.org/10.1007/s002220050088
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DOI: https://doi.org/10.1007/s002220050088