On C 1 -stability and C 1 -determinacy
Publications Mathématiques de l'IHÉS, Tome 70 (1989), pp. 5-46.
@article{PMIHES_1989__70__5_0,
     author = {Du Plessis, A. A. and Wall, C. T. C.},
     title = {On $C^1$-stability and $C^1$-determinacy},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--46},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {70},
     year = {1989},
     mrnumber = {1067379},
     zbl = {0712.58010},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1989__70__5_0/}
}
TY  - JOUR
AU  - Du Plessis, A. A.
AU  - Wall, C. T. C.
TI  - On $C^1$-stability and $C^1$-determinacy
JO  - Publications Mathématiques de l'IHÉS
PY  - 1989
SP  - 5
EP  - 46
VL  - 70
PB  - Institut des Hautes Études Scientifiques
UR  - http://www.numdam.org/item/PMIHES_1989__70__5_0/
LA  - en
ID  - PMIHES_1989__70__5_0
ER  - 
%0 Journal Article
%A Du Plessis, A. A.
%A Wall, C. T. C.
%T On $C^1$-stability and $C^1$-determinacy
%J Publications Mathématiques de l'IHÉS
%D 1989
%P 5-46
%V 70
%I Institut des Hautes Études Scientifiques
%U http://www.numdam.org/item/PMIHES_1989__70__5_0/
%G en
%F PMIHES_1989__70__5_0
Du Plessis, A. A.; Wall, C. T. C. On $C^1$-stability and $C^1$-determinacy. Publications Mathématiques de l'IHÉS, Tome 70 (1989), pp. 5-46. http://www.numdam.org/item/PMIHES_1989__70__5_0/

[1] Boardman, J. M., Singularities of differentiable maps, Publ. Math. IHES, 33 (1967), 21-57. | Numdam | MR | Zbl

[2] Brodersen, H., On finite and infinite Ck-A determinacy, Univ. of Oslo, preprint series, 1984, No. 14.

[3] Damon, J. N., Topological stability in the nice dimensions, Topology, 18 (1979), 129-142. | MR | Zbl

[4] Dimca, A., and Gibson, C. G., Classification of equidimensional contact-unimodular map-germs, Math. Scand., 56 (1985), 15-28. | MR | Zbl

[5] Dixmier, J., and Raynaud, M., Sur le quotient d'une variété algébrique par un groupe algébrique, in Mathematical Analysis and Applications, Adv. on Math. Supp. Studies, vol. 7A, Academic Press, 1981, 327-344. | Zbl

[6] Gibson, C. G., Wirthmüller, K., Du Plessis, A. A., Looijenga, E. J. N., Topological stability of smooth mappings, Springer LN M, 552, Springer Verlag, 1976. | MR | Zbl

[7] Hirsch, M. W., Differential topology, Springer GTM, 33, Springer Verlag, 1976. | MR | Zbl

[8] Mather, J. N., Stability of C∞ mappings, I. Ann. of Math., 87 (1968), 89-104 ; II. Ann. of Math., 89 (1969), 259-291 ; III. Publ. Math. IHES, 35 (1969), 127-156 ; IV. Publ. Math. IHES, 37 (1970), 223-248 ; V. Adv. in Math., 4 (1970), 301-335 ; VI. Springer LNM, 192, Springer Verlag, 1971, 207-255. | MR | Zbl

[9] Mather, J. N., Stratifications and mappings, Proc. Conf. on Dynamical Systems, ed. M. M. Peixoto, Academic Press, 1973, 195-232. | MR | Zbl

[10] Mather, J. N., How to stratify mappings and jet-spaces, Springer LNM 535, Springer Verlag, 1976, 128-176. | MR | Zbl

[11] Mather, J. N., Some non-finitely determined map-germs, Symposia Mathematica, II (1969), 303-320. | MR | Zbl

[12] May, R. D., Transversality properties of topologically stable mappings, Thesis, Harvard Univ., 1973 ; see also Stability and Transversality, Bull. AMS, 80 (1974), 85-89. | Zbl

[13] Morlet, C., Le lemme de Thom et les théorèmes de plongement de Whitney, I. Séminaire Henri-Cartan, 4 (1961-1962). | Numdam | Zbl

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

[15] Du Plessis, A., Genericity and smooth finite determinacy, Proc. Symp. Pure Math. AMS, 40, I (1983), 295-312. | MR | Zbl

[16] Du Plessis, A., On mappings of finite codimension, Proc. LMS, 50 (1985), 114-130. | MR | Zbl

[17] Du Plessis, A., and Wilson, L., On right-equivalence, Math. Z., 190 (1985), 163-205. | EuDML | MR | Zbl

[18] Porteons, I. R., Simple singularities of maps, Springer LNM, 192, Springer Verlag, 1971, 286-307. | MR | Zbl

[19] Steenrod, N., The topology of fibre bundles, Princeton, Math. Series 14, Princeton UP, 1951. | MR | Zbl

[20] Thom, R., and Levine, H., Singularities of differentiable mappings, Bonn. Math. Schrift, 6 (1959), republished in Springer LNM, 192, Springer Verlag, 1971, 1-89. | Zbl

[21] Thom, R., Local topological properties of differentiable mappings, Coll. on Differential Analysis, Tata Inst., OUP, 1964, 191-202. | MR | Zbl

[22] Varchenko, A. N., Local topological properties of analytic mappings, Math. USSR-Izv., 7 (1973), 883-917. | MR | Zbl

[23] Varchenko, A. N., Local topological properties of differentiable mappings, Math. USSR-Izv., 8 (1974), 1033-1082. | Zbl

[24] Wall, C. T. C., Stability pencils and polytopes, Bull. LMS, 12 (1980), 401-421. | MR | Zbl

[25] Wall, C. T. C., Classification of unimodal isolated singularities of complete intersections, Proc. Symp. Pure Math. AMS, 40, 2 (1983), 625-640. | MR | Zbl

[26] Wall, C. T. C., Determination of the semi-nice dimensions, Math. Proc. Camb. Phil. Soc., 97 (1985), 79-88. | MR | Zbl

[27] Wall, C. T. C., Finite determinacy of smooth map-germs, Bull. LMS, 13 (1981), 481-539. | MR | Zbl

[28] Wilson, L. C., Infinitely determined map-germs, Canad. J. Math., 33 (1981), 671-684. | MR | Zbl