On fibers of fat associated bundles
Volume 150 / 2017
Colloquium Mathematicum 150 (2017), 149-159
MSC: Primary 57S30; Secondary 22F30, 22E40, 22E46.
DOI: 10.4064/cm7138s-1-2017
Published online: 1 September 2017
Abstract
We are interested in associated fat bundles, which are an important tool in constructing Riemannian metrics of positive and non-negative curvature. We want to understand the behavior of the fatness condition under changes of structure groups of bundles. We show that if the structure group does not coincide with the holonomy group, and the $G$-bundle is fat, then the fiber of the bundle must be finitely covered by a sphere or a complex projective space of a particular dimension.
