On the Hopf conjecture with symmetry

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

The Hopf conjecture states that an even-dimensional, positively curved Riemannian manifold has positive Euler characteristic. We prove this conjecture under the additional assumption that a torus acts by isometries and has dimension bounded from below by a logarithmic function of the manifold dimension. The main new tool is the action of the Steenrod algebra on cohomology.

Original languageEnglish (US)
Pages (from-to)563-593
Number of pages31
JournalGeometry and Topology
Volume17
Issue number1
DOIs
StatePublished - Apr 8 2013
Externally publishedYes

Keywords

  • Grove program
  • Hopf conjecture
  • Positive sectional curvature
  • Steenrod algebra

ASJC Scopus subject areas

  • Geometry and Topology

Fingerprint Dive into the research topics of 'On the Hopf conjecture with symmetry'. Together they form a unique fingerprint.

  • Cite this