Fundamental Groups of Manifolds with Positive Sectional Curvature and Torus Symmetry

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Abstract

In 1965, Chern posed a question concerning the extent to which fundamental groups of manifolds admitting positive sectional curvature look like spherical space form groups. The original question was answered in the negative by Shankar in 1998, but there are a number of positive results in the presence of symmetry. These classifications fall into categories according to the strength of their conclusions. We give an overview of these results in the case of torus symmetry and prove new results in each of these categories.

Original languageEnglish (US)
Pages (from-to)2894-2925
Number of pages32
JournalJournal of Geometric Analysis
Volume27
Issue number4
DOIs
StatePublished - Oct 1 2017
Externally publishedYes

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Keywords

  • Chern problem
  • Fundamental groups
  • Isometric torus actions
  • Positive sectional curvature
  • Secondary cohomology operations

ASJC Scopus subject areas

  • Geometry and Topology

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