Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-22T23:21:16.797Z Has data issue: false hasContentIssue false
  • English
  • Français

Extension theorems for smooth functions on real analytic spaces and quotients by Lie groups and smooth stability

Published online by Cambridge University Press:  09 April 2009

G. S. Wells
G. S. Wells
Affiliation:
Department of Mathematics, University of Witwatersrand, Johannesburg, South Africa.
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.

Extension theorems are proved for smooth functions on a coherent real analytic space for which local defining functions exist which are finitely determined in the sense of J. Mather, (1968), and for smooth functions invariant under the action of a compact lie group G. thus providing the main step in the proof that smooth infinitesimal stability implies smooth stability in the appropriate categories. In addition the remaining step for the category of CxG-manifolds of finite orbit type is filled in.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 4 , December 1977 , pp. 440 - 457
Copyright
Copyright © Australian Mathematical Society 1977

References

Dieudonné, J. A. and Carrell, J. B. (1970). ‘Invariant theory old and new’, Advances in Maths 4, 1–80.CrossRefGoogle Scholar
Malgrange, B. (1966), Ideals of differentiable functions, (Oxford University Press).Google Scholar
Mather, J. N. (1969), ‘Stability of C∞ mappings II, Infinitesimal stability implies stability’, Ann. of Math. 89, 254–291.CrossRefGoogle Scholar
Mather, J. N. (1968), ‘Stability of C∞ mappings III, Finitely determined map germs’, Pub. Math. I.H.E.S. 35, 127–156.Google Scholar
Mather, J. N. (1970), ‘Stability of C∞ mappings IV, Classification of stable germs by R-algebras’, Pub. Math. I.H.E.S. 37, 223–248.Google Scholar
Mather, J. N. (1970), ‘Stability of C∞ mappings V, Transversality’ Advances in Math. 4, 301–336.CrossRefGoogle Scholar
Mather, J. N. (1973), Stratifications and mappings, Dynamical systems, ed. Peixoto, M. M., (Academic Press), 195–232.Google Scholar
Poenaru, V. (1975), ‘Stability of equivariant smooth maps’, Bull. Amer. Math. Soc. 81, 1125–1127.CrossRefGoogle Scholar
Tougeron, J-C (1972), Idéaux de foncrions différentiables, (Springer).Google Scholar
Schwarz, G. W. (1975), ‘Smooth functions invariant under the action of a compact lie group’, Topology 14, 63–68.CrossRefGoogle Scholar
Wall, C. T. C. (1971), ‘Lectures on Cx-stability and classification’, Proc. Liv. Singularities Symp. 1, (Springer Lecture Notes in Maths 192), 178–206.Google Scholar
Wells, G. S., ‘Spaces of smooth functions on analytic sets’, Bull. Amer. Math. Soc. 83 (1977), 276–278.CrossRefGoogle Scholar
Wells, G. S. (preprint), ‘Stability of smooth mappings on real semianalytic sets’.Google Scholar