On C 1 -stability and C 1 -determinacy

A. A. Du Plessis; C. T. C. Wall

Publications Mathématiques de l'IHÉS (1989)

  • Volume: 70, page 5-46
  • ISSN: 0073-8301

How to cite

top

Du Plessis, A. A., and Wall, C. T. C.. "On $C^1$-stability and $C^1$-determinacy." Publications Mathématiques de l'IHÉS 70 (1989): 5-46. <http://eudml.org/doc/104062>.

@article{DuPlessis1989,
author = {Du Plessis, A. A., Wall, C. T. C.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {C-determinacy; unfolding; Thom-Boardman variety; -stable maps},
language = {eng},
pages = {5-46},
publisher = {Institut des Hautes Études Scientifiques},
title = {On $C^1$-stability and $C^1$-determinacy},
url = {http://eudml.org/doc/104062},
volume = {70},
year = {1989},
}

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
PB - Institut des Hautes Études Scientifiques
VL - 70
SP - 5
EP - 46
LA - eng
KW - C-determinacy; unfolding; Thom-Boardman variety; -stable maps
UR - http://eudml.org/doc/104062
ER -

References

top
  1. [1] BOARDMAN, J. M., Singularities of differentiable maps, Publ. Math. IHES, 33 (1967), 21-57. Zbl0165.56803MR37 #6945
  2. [2] BRODERSEN, H., On finite and infinite Ck-A determinacy, Univ. of Oslo, preprint series, 1984, No. 14. 
  3. [3] DAMON, J. N., Topological stability in the nice dimensions, Topology, 18 (1979), 129-142. Zbl0454.58003MR80h:58015
  4. [4] DIMCA, A., and GIBSON, C. G., Classification of equidimensional contact-unimodular map-germs, Math. Scand., 56 (1985), 15-28. Zbl0579.32014MR87a:58027
  5. [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. Zbl0473.14019
  6. [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. Zbl0377.58006MR55 #9151
  7. [7] HIRSCH, M. W., Differential topology, Springer GTM, 33, Springer Verlag, 1976. Zbl0356.57001MR56 #6669
  8. [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. Zbl0216.20801MR38 #726
  9. [9] MATHER, J. N., Stratifications and mappings, Proc. Conf. on Dynamical Systems, ed. M. M. Peixoto, Academic Press, 1973, 195-232. Zbl0286.58003MR51 #4306
  10. [10] MATHER, J. N., How to stratify mappings and jet-spaces, Springer LNM 535, Springer Verlag, 1976, 128-176. Zbl0398.58008MR56 #13259
  11. [11] MATHER, J. N., Some non-finitely determined map-germs, Symposia Mathematica, II (1969), 303-320. Zbl0187.20504MR41 #4564
  12. [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. Zbl0281.58005
  13. [13] MORLET, C., Le lemme de Thom et les théorèmes de plongement de Whitney, I. Séminaire Henri-Cartan, 4 (1961-1962). Zbl0121.39902
  14. [14] DU PLESSIS, A., On the genericity of topologically finitely-determined map-germs, Topology, 21 (1982), 131-156. Zbl0499.58007MR83e:58010
  15. [15] DU PLESSIS, A., Genericity and smooth finite determinacy, Proc. Symp. Pure Math. AMS, 40, I (1983), 295-312. Zbl0523.58009MR85c:58016
  16. [16] DU PLESSIS, A., On mappings of finite codimension, Proc. LMS, 50 (1985), 114-130. Zbl0559.58006MR86d:58008
  17. [17] DU PLESSIS, A., and WILSON, L., On right-equivalence, Math. Z., 190 (1985), 163-205. Zbl0593.58014MR87d:58027
  18. [18] PORTEONS, I. R., Simple singularities of maps, Springer LNM, 192, Springer Verlag, 1971, 286-307. Zbl0221.57016MR45 #2723
  19. [19] STEENROD, N., The topology of fibre bundles, Princeton, Math. Series 14, Princeton UP, 1951. Zbl0054.07103MR12,522b
  20. [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. Zbl0216.45803
  21. [21] THOM, R., Local topological properties of differentiable mappings, Coll. on Differential Analysis, Tata Inst., OUP, 1964, 191-202. Zbl0151.32002MR33 #3307
  22. [22] VARCHENKO, A. N., Local topological properties of analytic mappings, Math. USSR-Izv., 7 (1973), 883-917. Zbl0291.32010MR48 #9754
  23. [23] VARCHENKO, A. N., Local topological properties of differentiable mappings, Math. USSR-Izv., 8 (1974), 1033-1082. Zbl0313.58009
  24. [24] WALL, C. T. C., Stability pencils and polytopes, Bull. LMS, 12 (1980), 401-421. Zbl0433.58006MR82h:58009
  25. [25] WALL, C. T. C., Classification of unimodal isolated singularities of complete intersections, Proc. Symp. Pure Math. AMS, 40, 2 (1983), 625-640. Zbl0519.58013MR85c:32018
  26. [26] WALL, C. T. C., Determination of the semi-nice dimensions, Math. Proc. Camb. Phil. Soc., 97 (1985), 79-88. Zbl0568.58008MR86c:58011
  27. [27] WALL, C. T. C., Finite determinacy of smooth map-germs, Bull. LMS, 13 (1981), 481-539. Zbl0451.58009MR83i:58020
  28. [28] WILSON, L. C., Infinitely determined map-germs, Canad. J. Math., 33 (1981), 671-684. Zbl0476.58005MR82k:58023

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.