A note on Pontrjagin forms

Mahuya Datta
2000 Proceedings of the American Mathematical Society  
Let P be a principal O(2m) bundle over a manifold M of dimension 4m, and let p be its m-dimensional Pontrjagin class. In this paper, we aim at answering the following question: Which representatives of the class p can be realised as the Pontrjagin form of some connection on P ?
doi:10.1090/s0002-9939-00-05732-4 fatcat:ureb4foarvew7irwmh4zcivbrq