Formality of Positive Quaternion Kaehler Manifolds

TL;DR

This paper proves that positive quaternion Kähler manifolds are formal spaces using Rational Homotopy Theory, providing new insights into their geometric structure and supporting the conjecture that they are symmetric spaces.

Contribution

The paper introduces a novel approach via Rational Homotopy Theory to prove the formality of positive quaternion Kähler manifolds, advancing understanding in differential geometry.

Findings

Positive quaternion Kähler manifolds are formal spaces.

Formality is preserved under spherical fibrations.

Supports the conjecture that these manifolds are symmetric spaces.

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.