A characterization of 𝐶^{∞}-sufficient 𝑘-jets

Kucharz, Wojciech

doi:10.1090/S0002-9939-1976-0400291-3

A characterization of $C\sp{\infty }$ -sufficient -jets

Author: Wojciech Kucharz
Journal: Proc. Amer. Math. Soc. 55 (1976), 419-423
MSC: Primary 58C25
DOI: https://doi.org/10.1090/S0002-9939-1976-0400291-3
MathSciNet review: 0400291
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Abstract: We improve some results of Mather and Arnold and find several necessary and sufficient conditions of sufficiency of -jets. As a corollary we prove that the set of ${C^\infty }$ -sufficient -jets is a semialgebraic subset of the space of -jets of ${C^\infty }$ mappings $F:({R^n},0) \to (R,0)$ .

[1] V. I. Arnol′d, Normal forms of functions near degenerate critical points, the Weyl groups 𝐴_{𝑘},𝐷_{𝑘},𝐸_{𝑘} and Lagrangian singularities, Funkcional. Anal. i Priložen. 6 (1972), no. 4, 3–25 (Russian). MR 0356124
[2] P. Mazet, Propriétés de 𝑂(𝐸) vis-a-vis des décompositions primaires, Séminaire Pierre Lelong (Analyse), Année 1970–1971, Springer, Berlin, 1972, pp. 71–81. Lecture Notes in Math., Vol. 275 (French). MR 0440070
[3] J. Mather, Stability of ${C^\infty }$ mappings. III, Iv, Inst. Hautes Études Sci. Publ. Math. No. 35 (1968), 279-308; ibid. No. 37 (1969), 223-248. MR 43 #1215a, b.
[4] J. Mather, Unpublished notes on right-equivalence.
[5] A. Seidenberg, A new decision method for elementary algebra, Ann. of Math. (2) 60 (1954), 365–374. MR 0063994, https://doi.org/10.2307/1969640