Positive curvature, local and global symmetry, and fundamental groups

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26 Scopus citations


A π1-invariant torus-action on a manifold M is a Tk-action on the universal covering which extends to the action of a semi-direct product π1(M) ⋉ ρ Tk. In particular, the Tk-action is the lift of a Tk-action on M if ρ is the identity map. The main result asserts that if a compact manifold Mn of positive sectional curvature admits a π1-invariant isometric Tk-action, then the fundamental group has a cyclic subgroup of index ≤ w(n). This refines the main result in [Ro1].

Original languageEnglish (US)
Pages (from-to)931-943
Number of pages13
JournalAmerican Journal of Mathematics
Issue number5
StatePublished - Oct 1999

All Science Journal Classification (ASJC) codes

  • General Mathematics


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