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Finite determinacy and topological triviality. I. (English) Zbl 0489.58003


MSC:

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
32S30 Deformations of complex singularities; vanishing cycles
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[1] Damon, J.: Finite Determinacy and Topological Triviality, preliminary announcement, preprint · Zbl 0489.58003
[2] Damon, J.: Topological Stability in the Nice Dimensions, Topology,18, 129-142 (1979) · Zbl 0454.58003 · doi:10.1016/0040-9383(79)90031-4
[3] Gaffney, T.: Thesis, Brandeis University, 1975
[4] 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
[5] Lê D?ng Tràng, Ramanujam, C.P.: The Invariance of Milnor’s Number Implies the Invariance of Topological Type. Amer. J. Math.98, 67-78 (1976) · Zbl 0351.32009 · doi:10.2307/2373614
[6] Looijenga, E.: Semi-Universal Deformation of a Simple Elliptic Singularity: Part 1-Unimodularity. Topology16, 257-262 (1977) · Zbl 0373.32004 · doi:10.1016/0040-9383(77)90006-4
[7] Mather, J.: Stability ofC ?-Mappings. II. Infinitesimal Stability Implies Stability, Ann. of Math.89, 254-291 (1969); III. Finitely Determined Map Germs, Publ. Math., I.H.E.S.35, 127-156 (1968); IV. Classification of Stable Germs by ?-algebras, Publ. Math. I.H.E.S.37, 223-248 (1979); V. Transversality, Advances in Math.4, 301-336 (1970) · Zbl 0177.26002 · doi:10.2307/1970668
[8] Mather, J.: Generic Projections, Ann. of Math.98, 226-245 (1973) · doi:10.2307/1970783
[9] Mather, J.: Stratifications and Mappings, Dynamical Systems Conf., M. Peixoto, ed. pp. 195-232. (Salvador Brazil), New York-London: Academic Press, 1973
[10] Martinet, J.: Deploiements Versels des Applications Differentiables et Classification des Applications Stables, Singularities d’Applications Differentiables, Plans-sur-Bex. Springer Lecture Notes 535, pp. 1-44, 1975
[11] Pinkham, H.: Deformations of Algebraic Varieties withG m -action, Asterisque20, 1-131 (1974) · Zbl 0304.14006
[12] Teissier, B.: Cycles Evanescents, Sections Planes, et Conditions de Whitney, Singularities a Cargese, Asterisque7, 8 285-362 (1973) · Zbl 0295.14003
[13] Timourian, J.G.: Invariance of Milnor’s Number Implies Topological Triviality, Amer J. Math.99, 437-446 (1977) · Zbl 0373.32003 · doi:10.2307/2373829
[14] Tougeron, J.C.: Ideaux de Fonctions Differentiables, Ergebnisse der Math. Band 71 Heidelberg-New York: Springer-Verlag 1972 · Zbl 0251.58001
[15] Wall, C.T.C.: Lectures onC ?-stability and Classification, Liverpool Singularities Symposium, Springer Lecture Notes, 192, pp. 178-206 (1970)
[16] Wirthmüller, K.: Universell Topologisch Triviale Deformationen, thesis, Univ. of Regensburg
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