Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A characterization for spaces of sections


Author: Palanivel Manoharan
Journal: Proc. Amer. Math. Soc. 126 (1998), 1205-1210
MSC (1991): Primary 58D15
DOI: https://doi.org/10.1090/S0002-9939-98-04246-4
MathSciNet review: 1443842
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The space of smooth sections of a bundle over a compact smooth manifold $K$ can be equipped with a manifold structure, called an $A$-manifold, where $A$ represents the Fréchet algebra of real valued smooth functions on $K$. We prove that the $A$-manifold structure characterizes the spaces of sections of bundles over $K$ and its open subspaces. We also describe the $A^{(r)}$-maps between $A$-manifolds.


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

  • 1. Hamilton, R.S.: The inverse function theorem of Nash and Moser. Bull. Am. Math. Soc. 7 no. 1, 65-222 (1982). MR 83j:58014
  • 2. Kobayashi, S.: Manifolds over function algebras and mapping spaces. Tôhoku Math. J. 41, 263-282 (1989). MR 90g:58014
  • 3. Manoharan, P.: A non-linear version of Swan's theorem. Math. Z. 209, 467-479 (1992). MR 93d:55019
  • 4. Manoharan, P.: Generalized Swan's theorem and its application. Proc. Amer. Math. Soc. 123, no. 10, 3219-3223 (1995). MR 95m:58020
  • 5. Milnor, J.W. and Stasheff, J.D.: Characteristic classes, Princeton University Press, 1974. MR 55:13428
  • 6. Swan, R.G.: Vector bundles and projective modules. Trans. Amer. Math. Soc. 105, 264-277 (1962). MR 26:785

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58D15

Retrieve articles in all journals with MSC (1991): 58D15


Additional Information

Palanivel Manoharan
Affiliation: Department of Mathematics, Kent State University, East Liverpool, Ohio 43920
Address at time of publication: College of Arts and Sciences, Florida Gulf Coast University, Fort Myers, Florida 33965
Email: manohara@mcs.kent.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04246-4
Keywords: $A$-manifold, $A$-map, $A^{(r)}$-map
Received by editor(s): February 6, 1996
Received by editor(s) in revised form: September 17, 1996
Additional Notes: The author was partially supported by NSF grant DMS-9401582
The abstract was presented in the Joint Math Meeting, Orlando, January 1996
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society