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A note on Pontrjagin forms


Author: Mahuya Datta
Journal: Proc. Amer. Math. Soc. 128 (2000), 3723-3729
MSC (2000): Primary 58J99, 53C23, 53C05
DOI: https://doi.org/10.1090/S0002-9939-00-05732-4
Published electronically: June 7, 2000
MathSciNet review: 1778283
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Abstract | References | Similar Articles | Additional Information

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 $P$?


References [Enhancements On Off] (What's this?)

  • [1] Mikhael Gromov: Partial Differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Folge, Band 9 (1986), Springer Verlag. MR 90a:58201
  • [2] M. Gromov and Ya. Eliashberg: Construction of a Smooth Mapping with a Prescribed Jacobian. I, Func. Anal. and Applications 7(1973), pp.423-434. MR 50:5841
  • [3] S. Kobayashi, K. Nomizu: Foundations of Differential Geometry (v. 1, 2) Interscience Tracts in Pure and Applied Mathematics (1969), John Wiley and Sons. MR 38:6501; MR 97c:53001a
  • [4] Izu Vaisman: Symplectic Geometry and Secondary Characteristic Classes, Progress in Mathematics 72 (1987), Birkhäuser. MR 89f:58062

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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: https://doi.org/10.1090/S0002-9939-00-05732-4
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

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