Positive curvature and symmetry in small dimensions

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Extending existing work in small dimensions, Dessai computed the Euler characteristic, signature, and elliptic genus for 8-manifolds of positive sectional curvature in the presence of torus symmetry. He also computes the diffeomorphism type by restricting his results to classes of manifolds known to admit non-negative curvature, such as biquotients. The first part of this paper extends Dessai's calculations to even dimensions up to 16. In particular, we obtain a first characterization of the Cayley plane in such a setting. The second part studies a closely related family of manifolds called positively elliptic manifolds, and we prove a conjecture of Halperin in this context for dimensions up to 16 or Euler characteristics up to 16.

Original languageEnglish (US)
Article number1950053
JournalCommunications in Contemporary Mathematics
Volume22
Issue number6
DOIs
StatePublished - Sep 1 2020

Keywords

  • Euler characteristic
  • Halperin conjecture
  • Positive sectional curvature
  • biquotient
  • elliptic genus
  • torus symmetry

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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