Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-12T07:24:59.313Z Has data issue: false hasContentIssue false
  • English
  • Français

Rigid and Finitely V-Determined Germs of C∞-Mappings

Published online by Cambridge University Press:  20 November 2018

Jacek Bochnak  and
Tzee-Char Kuo
Jacek Bochnak
Affiliation:
Université de Paris, 91-Orsay, France
Tzee-Char Kuo
Affiliation:
Institut des Hautes Études Scientifiques, 91-Bures-sur-Yvette, France
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.

Let (respectively ) denote the ring of germs at 0 ∈ Rn of all C∞ functions (respectively Cμ functions) from Rn to R. For a given where is the space of all germs of C∞ mappings Rn → Rp, let J(φ) denote the ideal in generated by φ1, … , φp and the Jacobian determinants

where Let

Clearly, is an ideal in and where is the (unique) maximal ideal of .

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 727 - 732
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bochnak, J. and Lojasiewicz, S., A converse of the Kuiper-Kuo theorem, Proc. of Liverpool Singularities - Symp. I, Lectures Notes in Math. 192 (1971), 254–261.Google Scholar
2. Bochnak, J. and Kuo, T.-C., Different realization of a non sufficient jet, Indag. Math. 84 (1972), 24–31.Google Scholar
3. Bochnak, J., Jets suffisants et germes de determination finie, C.R. Acad. Sci. Paris Sér. A-B 271 (1970), 1162–1164.Google Scholar
4. Bochnak, J., Relevements des jets, Séminaire Pierre Lelong (Analyse), 1971, Lectures Notes in Math. 275, Springer-Verlag (1972), 106–118.Google Scholar
5. Kuiper, N., C1-equivalence of functions near isolated critical points, Symp. Infinite Dimensional Topology, Baton Rouge, Ann. of Math. Studies 69 (Princeton Univ. Press, 1972), 199–218.Google Scholar
6. Kuo, T.-C., On C°-sufficiency of jets of potential functions, Topology 8 (1969), 167–171.Google Scholar
7. Kuo, T.-C., A complete determination of C°-sufficiency in Jr(2, 1), Invent. Math 8 (1969), 226–235.Google Scholar
8. Kuo, T.-C., Characterization of V-sufficiency of jets, Topology 11 (1972), 115–131.Google Scholar
9. Mather, J., Stability of C*-mappings. Ill, Publication I.H.E.S. 85 (1969), 278–308.Google Scholar
10. Merrien, J. and Tougeron, J. C., Idéaux de fonctions differentiates. II, Ann. Inst. Fourier (Grenoble) 20 (1970), 179–233.Google Scholar
ll. Schreier, O. and Sperner, E., Introduction to modern algebra and matrix theory (Chelsea, New- York, 1951).Google Scholar
12. Thorn, R., Local topological properties of differentiable mappings, Differential Analysis, Bombay Colloquim 1964 (Oxford Univ. Press, Oxford, 1965).Google Scholar
13. Tougeron, J. C., Idéaux de fonctions differentiable s. I, Ann. Inst. Fourier (Grenoble) 18 (1968), 177–140.Google Scholar