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 language | English (US) |
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Article number | 1950053 |
Journal | Communications in Contemporary Mathematics |
Volume | 22 |
Issue number | 6 |
DOIs | |
State | Published - Sep 1 2020 |
Keywords
- Euler characteristic
- Halperin conjecture
- Positive sectional curvature
- biquotient
- elliptic genus
- torus symmetry
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics