On définit une caractéristique d’Euler généralisée pour les ensembles symétriques par arcs équipés d’une action de groupe. Elle coïncide avec la série de Poincaré en homologie équivariante pour les ensembles compacts et non singuliers, mais reste différente en général. On met l’accent sur le cas de et on donne une application à l’étude des singularités des germes de fonctions de Nash avec un analogue des fonctions zêta motiviques de Denef et Loeser.
We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of , and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.
@article{AIF_2008__58_1_1_0,
author = {Fichou, Goulwen},
title = {Equivariant virtual Betti numbers},
journal = {Annales de l'Institut Fourier},
volume = {58},
year = {2008},
pages = {1-27},
doi = {10.5802/aif.2342},
zbl = {1142.14003},
mrnumber = {2401214},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2008__58_1_1_0}
}
Fichou, Goulwen. Equivariant virtual Betti numbers. Annales de l'Institut Fourier, Tome 58 (2008) pp. 1-27. doi : 10.5802/aif.2342. http://gdmltest.u-ga.fr/item/AIF_2008__58_1_1_0/
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