Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-29T00:58:44.782Z Has data issue: false hasContentIssue false
  • English
  • Français

Manifolds of smooth maps

Published online by Cambridge University Press:  17 April 2009

Truong Công Nghê
Truong Công Nghê
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales 2006, Australia.
Rights & Permissions [Opens in a new window]

Abstract

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.

We show that the space of smooth maps from a compact smooth manifold into another smooth manifold can be endowed with the structure of a smooth manifold if we use the Γ-differentiation of Yamamuro. We then generalise the Smale Density Theorem to mappings between these manifolds.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 1 - 11
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Abraham, R., Lectures of Smale on differential topology (Columbia University, New York, 1962).Google Scholar
[2]Abraham, Ralph, Robbin, Joel, Transversal mappings and flows (Benjamin, New York, Amsterdam, 1967).Google Scholar
[3]Fischer, H.R., “Differentialrechnung in lokalkonvexen Räumen und Mannigfaltigkeiten von Abbildungen” (Manuskripte d. Fakultät für Math. und Informatik, Univ. Mannheim, Mannheim [1977]).Google Scholar
[4]Gutknecht, Jürg, “Die -Struktur auf der Diffeomorphismengruppe einer kompakten Mannigfaltigkeit” (Doctoral Dissertation, Eidgenössische Technische Hochschule, Zürich, 1977).Google Scholar
[5]Gromol, D., Klingenberg, W., Meyer, W., Riemannsche Geometrie im Großen (Lecture Notes in Mathematics, 55. Springer-Verlag, Berlin, Heidelberg, New York, 1968).CrossRefGoogle Scholar
[6]Irwin, M.C., “On the smoothness of the composition map”, Quart. J. Math. Oxford Ser. 23 (1972), 113–133.CrossRefGoogle Scholar
[7]Keller, H.H., “Differential calculus in Fréchet spaces and manifolds of mappings” preprint.Google Scholar
[8]Leslie, J.A., “On a differential structure for the group of diffeomorphisms”, Topology 6 (1967), 263–271.CrossRefGoogle Scholar
[9]Michor, P., “Manifolds of smooth maps”, Cahiers Topologie Géom. Différentielle 19 (1978), 47–78.Google Scholar
[10]Nghê, Truong Công, “Differentiable manifolds modelled on locally convex spaces” (PhD thesis, Australian National University, Canberra, 1977). See also: Abstract, Bull. Austral. Math. Soc. 18 (1978), 303–304.CrossRefGoogle Scholar
[11]Nghê, Truong Công and Yamamuro, S., “Locally convex spaces, differentiation and manifolds” Comment. Math. Special Issue 2 (1979), 229–338.Google Scholar
[12]Yamamuro, Sadayuki, A theory of differentiation in locally convex spaces (Memoirs of the American Mathematical Society, 212. American Mathematical Society, Providence, Rhode Island, 1979).Google Scholar