Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-22T07:33:28.334Z Has data issue: false hasContentIssue false
  • English
  • Français

A De Rham Theorem for Generalised Manifolds

Published online by Cambridge University Press:  20 January 2009

Maria Elena Verona
Maria Elena Verona
Affiliation:
Centrul de Statisticǎ Matematicǎ, Str. Stirbei Vodǎ 174, Bucharest
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In (2) Bruhat has developed a theory of differentiable functions and distributions on a locally compact group in order to apply it to the study of the irreducible representations of the p-adic groups. Later, Whyburn (8) defined differentiable forms on a locally compact group and proved an analog of the de Rham theorem concerningthe relationship between the Čech cohomology and the De Rham cohomology. In (4) Ihave introduced the notions of “generalised manifold” (roughly speaking a projective limit of smooth manifolds) and of “differentiable forms” on it, extending some of the results due to Bruhat and Whyburn.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 127 - 135
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1)Bourbaki, N., Topologie Générate (Hermann, Paris).Google Scholar
(2)Bruhat, F., Distributions sur un groupe localement compact et applications a l'etude des representations des groupes p-adiques, Bull. Soc. Math. France 89 (1961), 43–75.CrossRefGoogle Scholar
(3)Chevalley, C. and Eilenberg, S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948), 85–124.CrossRefGoogle Scholar
(4)Cioranu-Verona, M. E., Maps and forms on generalised manifolds (in Romanian), St. Cere. Mat. 26 (1974), 133–143.Google Scholar
(5)Godement, R., Theorie des Faisceaux (Hermann, Paris, 1974).Google Scholar
(6)Lashof, R., Lie algebras of locally compact groups, Pacific J. Math. 7 (1957), 1145-1162.CrossRefGoogle Scholar
(7)Montgomery, D. and Zippin, L., Topological Transformation Groups (Interscience, New York, 1955).Google Scholar
(8)Whyburn, K., Differentiable cohomology on locally compact groups, Proc. Nat. Acad. Sci. U.S.A. 67 (1970), 45–51.CrossRefGoogle ScholarPubMed