Basically, due to a famous result of Berger the possible holonomy groups of (simply connected) Riemannian manifolds are well-known. These special geometries featuring prominent examples like Kahler manifolds or Joyce manifolds often do possess remarkable topological properties. In this talk I shall discuss one property which virtually all these manifolds might have in common and which stems from Rational Homotopy Theory, namely formality. This expresses the fact that rationally the homotopy theory of these spaces might be no more complicated than their cohomology theory. I shall provide a general characterisation result on how formality behaves with respect to fibrations. As a very special case of this the formality of Positive Quaternion Kahler Manifolds can easily be deduced.
Geometry-Topology Seminar
Thursday, February 9, 2012 - 4:30pm
Manuel Amann
Univ. of Muenster and Penn