We will extend the infinitesimal criteria for the equisingularity (i.e. topological triviality) of deformations of germs of mappings , , to non-finitely determined germs (these occur generically outside the “nice dimensions” for Mather, even among topologically stable mappings). The failure of finite determinacy is described geometrically by the “versality discriminant”, which is the set of points where is not stable (i.e. viewed as an unfolding it is not versal). The criterion asserts that algebraic filtration conditions on the infinitesimal deformations together with topological triviality of in a “conical neighborhood” of the versality discriminant imply topological triviality of itself.
Nous étendons le critère infinitésimal par l’équisingularité (i.e. trivialité topologique) des déformations des germes d’applications , , à des germes qui ne sont pas de détermination finie (ils apparaissent génériquement en dehors des “bonnes dimensions” de Mather, même parmi les applications topologiquement stables). On décrit géométriquement le caractère non fini par le “discriminant versel”, qui représente l’ensemble des points où n’est pas stable (i.e. non versel lorsqu’on le regarde comme un déploiement). Ce critère affirme que des conditions de filtration algébrique sur les déformations infinitésimales associées à la trivialité topologique de dans un “voisinage conique” du discriminant versel entraîne la trivialité topologique de elle-même.
@article{AIF_1990__40_4_965_0, author = {Damon, James}, title = {The versality discriminant and local topological equivalence of mappings}, journal = {Annales de l'Institut Fourier}, pages = {965--1004}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {40}, number = {4}, year = {1990}, doi = {10.5802/aif.1244}, zbl = {0703.58005}, mrnumber = {92d:58014}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1244/} }
TY - JOUR AU - Damon, James TI - The versality discriminant and local topological equivalence of mappings JO - Annales de l'Institut Fourier PY - 1990 SP - 965 EP - 1004 VL - 40 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1244/ DO - 10.5802/aif.1244 LA - en ID - AIF_1990__40_4_965_0 ER -
%0 Journal Article %A Damon, James %T The versality discriminant and local topological equivalence of mappings %J Annales de l'Institut Fourier %D 1990 %P 965-1004 %V 40 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1244/ %R 10.5802/aif.1244 %G en %F AIF_1990__40_4_965_0
Damon, James. The versality discriminant and local topological equivalence of mappings. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 965-1004. doi : 10.5802/aif.1244. https://aif.centre-mersenne.org/articles/10.5802/aif.1244/
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