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
Full-text PDF Free Access

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) [Results in Mathematics and Related Areas (3)], vol. 9, Springer-Verlag, Berlin, 1986. MR 864505
  • [2] M. L. Gromov and Ja. M. Èliašberg, Construction of a smooth mapping with a prescribed Jacobian. I, Funkcional. Anal. i Priložen. 7 (1973), no. 1, 33–40 (Russian). MR 0353357
  • [3] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Interscience Tracts in Pure and Applied Mathematics, No. 15 Vol. II, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1969. MR 0238225
    Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1963 original; A Wiley-Interscience Publication. MR 1393940
  • [4] Izu Vaisman, Symplectic geometry and secondary characteristic classes, Progress in Mathematics, vol. 72, Birkhäuser Boston, Inc., Boston, MA, 1987. MR 932470

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58J99, 53C23, 53C05

Retrieve articles in all journals with MSC (2000): 58J99, 53C23, 53C05


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
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