Topological properties of positively curved manifolds with symmetry

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Manifolds admitting positive sectional curvature are conjectured to have rigid homotopical structure and, in particular, comparatively small Euler charateristics. In this article, we obtain upper bounds for the Euler characteristic of a positively curved Riemannian manifold that admits a large isometric torus action. We apply our results to prove obstructions to symmetric spaces, products of manifolds, and connected sums admitting positively curved metrics with symmetry.

Original languageEnglish (US)
Pages (from-to)1377-1405
Number of pages29
JournalGeometric and Functional Analysis
Volume24
Issue number5
DOIs
StatePublished - Sep 1 2014
Externally publishedYes

Keywords

  • Primary 53C20
  • Secondary 57N65

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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