Geometric formality of homogeneous spaces and of biquotients

D. Kotschick and S. Terzić

Vol. 249 (2011), No. 1, 157–176

DOI: 10.2140/pjm.2011.249.157

Abstract

We provide examples of homogeneous spaces that are neither symmetric spaces nor real cohomology spheres, yet have the property that every invariant metric is geometrically formal. We also extend the known obstructions to geometric formality to some new classes of homogeneous spaces and of biquotients, and to certain sphere bundles.

Keywords

formality, harmonic forms, homogeneous space, Stiefel manifold, biquotient

Mathematical Subject Classification 2000

Primary: 53C25, 53C30

Secondary: 57T15, 57T20, 58A10

Milestones

Received: 17 September 2009

Accepted: 4 January 2010

Published: 3 January 2011