Equivalence of generic mappings and ${C}^{\infty }$ normalization
Compositio Mathematica, Volume 49 (1983) no. 3, pp. 291-308.
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Gaffney, Terence; Wilson, Leslie. Equivalence of generic mappings and $C^\infty$ normalization. Compositio Mathematica, Volume 49 (1983) no. 3, pp. 291-308. http://archive.numdam.org/item/CM_1983__49_3_291_0/

[1] E. Bierstone and P. Milman: Composite differentiable functions. Lecture Notes, AMS Symposium on Singularities, Arcata, 1981. | MR

[2] E. Bierstone and G. Schwartz: The extension problem and related themes in differential analysis. Lecture Notes, AMS Symposium on Singularities, Arcata, 1981. | Zbl

[3] S. Blank: Extending immersions and regular homotopies in codimension 1. Ph.D. Thesis, Brandeis University, 1967.

[4] T. Bröcker: Differentiable germs and catastrophes. Translated by L. Lander, London Math. Society Lecture Notes Series 17, Cambridge University Press, 1975. | MR | Zbl

[5] J. Damon: The relation between C∞ and topological stability. Bol. Soc. Brasil. Mat. 8 (1977) 1-38. | Zbl

[6] A. Du Plessis: Genericity and smooth finite determinacy. In: AMS Proceedings of Symposia in Pure Mathematics 40 (1982). | MR | Zbl

[7] A. Du Plessis: On the genericity of topologically finitely-determined map-germs. Topology 21 (1982) 131-156. | MR | Zbl

[8] A. Du Plessis and H. Brodersen: On smooth ∞-determinacy and topological finite determinancy. Preliminary version.

[9] A. Du Plessis, T. Gaffney and L. Wilson: Map-germs determined by their discriminant. In preparation.

[10] A. Du Plessis and L. Wilson: Right-symmetry of map-germs. In Preparation.

[11] G. Francis and S. Troyer: Excellent maps with given folds and cusps. Houston J. Math. 3 (1977) 165-194. | MR | Zbl

[12] T. Gaffney: Properties of finitely determined germs. Ph.D. Thesis, Brandeis University, 1975.

[13] T. Gaffney and L. Wilson: Equivalence theorems in global singularity theory. AMS Symposium on Singularities, Arcata, Proceedings of Symposia in Pure Math. 40, to appear. | MR | Zbl

[14] D. Husemoller: Fibre bundles. Graduate texts in mathematics # 20, Springer-Verlag, New York, 1975. | MR | Zbl

[15] K. Jänich: Symmetry properties of singularities of C∞-functions. Math. Ann. 238 (1978) 147-156. | Zbl

[16] B. Malgrange: Ideals of differentiable functions. Oxford University Press, 1966. | MR | Zbl

[17] J. Merrien: Faisceaux analytiques semi-cohérent et fonctions différentiables. Thèse, Université de Rennes, 1980. Ann. Inst. Fourier 32, 2 (1982) 229-260. | Numdam | MR | Zbl

[18] R. Narasimhan: Introduction to the theory of analytic spaces. Lecture notes in mathematics no. 25, Springer-Verlag, New York, 1966. | MR | Zbl

[19] F. Pham: Remarque sur l'équivalence des fonctions de phase. C. R. Acad. Sci. Paris 290 (23 juin 1980) 1095-1097. | MR | Zbl

[20] B. Teissier: The hunting of invariants in the geometry of the discriminant. Real and complex singularities, P. Holm, ed., Sijthoff and Noordhoff, Alphen aan den Rijn, Netherlands, 1977. | MR

[21] J.C. Tougeron: Idéaux de fonctions différentiables. Ergebnisse Band 71, Springer-Verlag, New York, 1972. | MR | Zbl

[22] C.T.C. Wall: Finite determinacy of smooth map-germs. Bull. London Math. Soc. 13 (1981) 481-539. | MR | Zbl

[23] L. Wilson: Equivalence of stable mappings between two-dimensional manifolds. J. Differential Geom. 11 (1976) 1-14. | MR | Zbl

[24] L. Wilson: Global singularity theory. Institute of Mathematics, University of Aarhus (Denmark), Seminar Notes No. 1 (1982) 129-137. | Zbl

[25] K. Wirthmüller: Singularities determined by their discriminant. Math. Ann. 252 (1980) 237-245. | MR | Zbl

[26] O. Zariski and P. Samuel: Commutative algebra, II. Van Nostrand, New York, 1960. | MR | Zbl