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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 characterization for spaces of sections


Author: Palanivel Manoharan
Journal: Proc. Amer. Math. Soc. 126 (1998), 1205-1210
MSC (1991): Primary 58D15
MathSciNet review: 1443842
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-98-04246-4
PII: S 0002-9939(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