Positively curved manifolds with maximal discrete symmetry rank

Fuquan Fang, Xiaochun Rong

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 M2n admits an effective isometric ℤpk-action for a prime p ≥ p(n), then k ≤ n and "=" implies that M2n is homeomorphic to a sphere or a complex projective space. (2) If M2n+1 admits an isometric S1pk-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 languageEnglish (US)
Pages (from-to)227-245
Number of pages19
JournalAmerican Journal of Mathematics
Volume126
Issue number2
DOIs
StatePublished - Apr 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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