Document Zbl 0446.58004

On the determinacy of smooth map-germs. (English) Zbl 0446.58004

Invent. Math. 58, 107-160 (1980).

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MSC:

58C25	Differentiable maps on manifolds
58K99	Theory of singularities and catastrophe theory
57R45	Singularities of differentiable mappings in differential topology
57R35	Differentiable mappings in differential topology

Keywords:

orders of determinancy and normal forms for non-stable map germs; finitely-determined map germs

Citations:

Zbl 0159.250; Zbl 0202.551

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Full Text: DOI EuDML

References:

[1]	Arnol’d, V.I.: Normal forms of functions in neighbourhoods of degenerate critical points. Russian Math. Surveys 29, 10-50 (1974) · Zbl 0304.57018 · doi:10.1070/RM1974v029n02ABEH003846
[2]	Arnol’d, V.I.: Local normal forms of functions. Invent. math.35, 87-109 (1976) · Zbl 0336.57022 · doi:10.1007/BF01390134
[3]	Belitskii, G.R.: Equivalence and normal forms of germs of smooth mappings. Russian Math. Surveys33, 107-177 (1978) · Zbl 0398.58009 · doi:10.1070/RM1978v033n01ABEH002237
[4]	Bochnak, J., Kucharz, W.: Sur les germes d’applications différentiables à singularités isolées. Trans. AMS252, 115-131 (1979) · Zbl 0458.58006
[5]	Gaffney, T.: Properties of finitely-determined germs. Thesis, Brandeis University, 1975
[6]	Gaffney, T.: On the order of determination of a finitely-determined germ Invent. Math.37, 83-92 (1976) · Zbl 0354.58012 · doi:10.1007/BF01418963
[7]	Gaffney, T.: A note on the order of determination of a finitely-determined germ. Invent. Math.52, 127-130 (1979) · Zbl 0419.58004 · doi:10.1007/BF01403059
[8]	Gibson, C.G., Wirthmüller, K., du Plessis, A.A., Looijenga, E.J.N.: Topological stability of smooth mappings, Ch. III. Springer LNM 552. Berlin-Heidelberg-New York: Springer-Verlag 1976 · Zbl 0377.58006
[9]	Gomozov, E.P.: A versality theorem for a bilateral group of changes of variables. Funct. Anal. Appl.9, 332-333 (1975) · Zbl 0329.58004 · doi:10.1007/BF01075884
[10]	Latour, F.: Stabilité des champs d’applications différentiables; généralisation d’un théorème de J. Mather. Comptes Rendus Acad. Sci.268(A), 1331-1334 (1969) · Zbl 0184.48501
[11]	Martinet, J.: Deplorements versels des applications différentiables et classification des applications stables. In: Singularités d’Applications Différentiables (O. Burlet and F. Ronga, eds.) pp. 144, Springer LNM 535. Berlin-Heidelberg-New York: Springer-Verlag 1976
[12]	Martinet, J.: Deploiements stables des germes de type fini, et détermination finie des applications différentiables. Preprint, Université de Strasbourg, 1976 · Zbl 0431.58009
[13]	Mather, J.N.: Stability ofC ? mappings, III: finitely determined germs. Publ. Math. IHES35, 127-156 (1969) · Zbl 0159.25001
[14]	Mather, J.N.: Stability ofC ? mappings, IV: classification of stable germs by ?-algebras. Publ. Math. IHES37, 223-248 (1970) · Zbl 0202.55102
[15]	Mather, J.N.: Stability ofC ? mappings, VI: the nice dimensions. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971 · Zbl 0211.56105
[16]	Mather, J.N.: Generic Projections. Ann. of Math.98, 226-245 (1973) · doi:10.2307/1970783
[17]	Nirenberg, L.: A proof of the Malgrange Preparation Theorem. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971 · Zbl 0212.10702
[18]	Siersma, D.: Classification and deformation of singularities. Thesis, University of Amsterdam, 1974 · Zbl 0283.57012
[19]	Siersma, D.: Periodicities in Arnol’d’s lists of singularities. In: Real and complex singularities, Oslo 1976 (P. Holm, ed.) pp.497-524, Sijthoff & Noordhoff 1977
[20]	Wall, C.T.C.: Lectures onC ?-stability and classification. In: Proc. Liverpool Singularities Symp. I (C.T.C. Wall, ed.). Springer LNM 192. Berlin-Heidelberg-New York: Springer-Verlag 1971 · Zbl 0211.56104
[21]	Wall, C.T.C.: Are maps finitely determined in general? Bull. LMS11, 151-154 (1979) · Zbl 0431.58008
[22]	Wassermann, G.: Stability of Unfoldings. Springer LNM 393. Berlin-Heidelberg-New York: Springer-Verlag 1974 · Zbl 0288.57017

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