Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2025-01-03T18:42:30.149Z Has data issue: false hasContentIssue false
  • English
  • Français

Manifolds of smooth maps II: transversality

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 generalise the standard notion of transversality to maps between manifolds modelled on locally convex spaces and prove that all standard transversal theorems remain valid for this generalised notion.

As first applications, we use our generalised Transversal Density Theorem to prove several simple “generic” results for local smooth maps which parallel the usual ones.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 49 - 59
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Abraham, Ralph, Robbin, Joel, Transversal mappings and flows (Benjamin, New York, Amsterdam, 1967).Google Scholar
[2]Golubitsky, M., Guillemin, V., Stable mappings and their singularities (Graduate Texts in Mathematics, 14. Springer-Verlag, New York, Heidelberg, Berlin, 1973).CrossRefGoogle Scholar
[3]Hirsch, Morris W., Differential topology (Graduate Texts in Mathematics, 33. Springer-Verlag, New York, Heidelberg, Berlin, 1976).CrossRefGoogle Scholar
[4]Kurland, H. and Robbin, J., “Infinite codimension and transversality” Dynamical Systems, 135–150 (Proc. Sympos. University of Warwick, 1973/74. Lecture Notes in Mathematics, 468. Springer-Verlag, Berlin, Heidelberg, New York, 1975).Google Scholar
[5]Nghê, Truong Công, “Manifolds of smooth maps” Bull. Austral. Math. Soc. 24 (1981), 1–11.CrossRefGoogle Scholar
[6]Nghê, Truong Công and Yamamuro, S., “Locally convex spaces, differentiation and manifolds” Comment. Math. Special Issue 2 (1979), 229–338.Google Scholar
[7]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