A note on Pontrjagin forms

Abstract

Let P P be a principal O ( 2 m ) O(2m) bundle over a manifold M M of dimension 4 m 4m , and let p p be its m m -dimensional Pontrjagin class. In this paper, we aim at answering the following question: Which representatives of the class p p can be realised as the Pontrjagin form of some connection on P P ?