## Abstract

Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a constant p(n) > 0 such that (1) If M^{2n} admits an effective isometric ℤ_{p}^{k}-action for a prime p ≥ p(n), then k ≤ n and "=" implies that M^{2n} is homeomorphic to a sphere or a complex projective space. (2) If M^{2n+1} admits an isometric S^{1} ℤ_{p}^{k}-action for a prime p ≥ p(n), then k ≤ n and "=" implies that M is homeomorphic to a sphere. (3) For M in (1) or (2), if n ≥ 7 and k ≥ [3n/4] + 2, then M is homeomorphic to a sphere or homotopic to a complex projective space.

Original language | English (US) |
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Pages (from-to) | 227-245 |

Number of pages | 19 |

Journal | American Journal of Mathematics |

Volume | 126 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2004 |

## All Science Journal Classification (ASJC) codes

- General Mathematics