Formality of Positive Quaternion Kaehler Manifolds
arXiv:0911.3250
Abstract
Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We offer a new approach to this field of study via Rational Homotopy Theory, thereby proving the formality of Positive Quaternion Kaehler Manifolds. This result is established by means of an in-depth investigation on how formality behaves under spherical fibrations.
replaced by "On fibrations with formal elliptic fibers" arXiv:1112.3556v1 [math.AT]