Positive curvature and symmetry in small dimensions

Manuel Amann, Lee Kennard

Research output: Contribution to journalArticle

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)
JournalCommunications in Contemporary Mathematics
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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