On démontre que pour chaque entier il existe un voisinage ouvert de l’application identité de la 2-sphère, pour la topologie, tel que : si est un sous-groupe nilpotent à longueur de nilpotence , engendré par une famille quelconque d’éléments de , alors l’action naturelle de sur a un point fixe. De plus, en présence d’une orbite finie cette action a au moins deux points fixes.
We prove that for each integer there is an open neighborhood of the identity map of the 2-sphere , in topology such that: if is a nilpotent subgroup of with length of nilpotency, generated by elements in , then the natural -action on has nonempty fixed point set. Moreover, the -action has at least two fixed points if the action has a finite nontrivial orbit.
Classification : 37B05, 37C25, 37C85
Mots clés : action de groupe, groupe nilpotent, point fixe
@article{AIF_2002__52_4_1075_0, author = {Druck, Suely and Fang, Fuquan and Firmo, Sebasti\~ao}, title = {Fixed points of discrete nilpotent group actions on $$}, journal = {Annales de l'Institut Fourier}, pages = {1075--1091}, publisher = {Association des Annales de l'institut Fourier}, volume = {52}, number = {4}, year = {2002}, doi = {10.5802/aif.1912}, zbl = {1005.37019}, mrnumber = {1926674}, language = {en}, url = {aif.centre-mersenne.org/item/AIF_2002__52_4_1075_0/} }
Druck, Suely; Fang, Fuquan; Firmo, Sebastião. Fixed points of discrete nilpotent group actions on $$. Annales de l'Institut Fourier, Tome 52 (2002) no. 4, pp. 1075-1091. doi : 10.5802/aif.1912. https://aif.centre-mersenne.org/item/AIF_2002__52_4_1075_0/
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