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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Pontrjagin forms


Author: Mahuya Datta
Journal: Proc. Amer. Math. Soc. 128 (2000), 3723-3729
MSC (2000): Primary 58J99, 53C23, 53C05
Published electronically: June 7, 2000
MathSciNet review: 1778283
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Abstract:

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 $P$?


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Additional Information

Mahuya Datta
Affiliation: Department of Pure Mathematics, University College of Science, 35, P.Barua Sarani, Calcutta 700019, India
Email: mahuyad@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05732-4
PII: S 0002-9939(00)05732-4
Keywords: Principal bundles, connections, Pontrjagin class, $h$-principle
Received by editor(s): February 10, 1999
Published electronically: June 7, 2000
Additional Notes: This work was supported by the Commission on Development and Exchange of the International Mathematical Union
Communicated by: Christopher Croke
Article copyright: © Copyright 2000 American Mathematical Society