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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Connections with prescribed first Pontrjagin form
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by Mahuya Datta PDF
Trans. Amer. Math. Soc. 355 (2003), 3813-3824 Request permission

Abstract:

Let $P$ be a principal $O(n)$ bundle over a $C^\infty$ manifold $M$ of dimension $m$. If $n\geq 5m+4+4\binom {m+1}{4}$, then we prove that every differential 4-form representing the first Pontrjagin class of $P$ is the Pontrjagin form of some connection on $P$.
References
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Additional Information
  • Mahuya Datta
  • Affiliation: Department of Pure Mathematics, University of Calcutta, 35 P. Barua Sarani, Calcutta 700019, India
  • Email: mahuyad@hotmail.com
  • Received by editor(s): September 26, 2002
  • Received by editor(s) in revised form: February 14, 2003
  • Published electronically: May 15, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 3813-3824
  • MSC (2000): Primary 53C05, 53C23, 58J99
  • DOI: https://doi.org/10.1090/S0002-9947-03-03311-7
  • MathSciNet review: 1990175