On démontre que, pour une large classe de groupes, le nombre de Reidemeister d'un automorphisme ϕ est égal au nombre de points fixes de dimension finie de sur le dual unitaire, si l'un de ces nombres est fini. Ce théorème est une généralisation naturelle aux groupes infinis du théorème classique de Burnside–Frobenius. Il a des conséquences importantes en dynamique topologique.
It is proved for a wide class of groups that the Reidemeister number of an automorphism ϕ is equal to the number of finite-dimensional fixed points of on the unitary dual, if one of these numbers is finite. This theorem is a natural generalization to infinite groups of the classical Burnside–Frobenius theorem. It has important consequences in Topological Dynamics.
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@article{CRMATH_2008__346_19-20_1033_0,
author = {Fel'shtyn, Alexander and Troitsky, Evgenij},
title = {Th\'eorie de {Burnside{\textendash}Frobenius} tordue pour les groupes virtuellement polycycliques},
journal = {Comptes Rendus. Math\'ematique},
pages = {1033--1038},
publisher = {Elsevier},
volume = {346},
number = {19-20},
year = {2008},
doi = {10.1016/j.crma.2008.09.003},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.09.003/}
}
TY - JOUR AU - Fel'shtyn, Alexander AU - Troitsky, Evgenij TI - Théorie de Burnside–Frobenius tordue pour les groupes virtuellement polycycliques JO - Comptes Rendus. Mathématique PY - 2008 SP - 1033 EP - 1038 VL - 346 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.09.003/ DO - 10.1016/j.crma.2008.09.003 LA - fr ID - CRMATH_2008__346_19-20_1033_0 ER -
%0 Journal Article %A Fel'shtyn, Alexander %A Troitsky, Evgenij %T Théorie de Burnside–Frobenius tordue pour les groupes virtuellement polycycliques %J Comptes Rendus. Mathématique %D 2008 %P 1033-1038 %V 346 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.09.003/ %R 10.1016/j.crma.2008.09.003 %G fr %F CRMATH_2008__346_19-20_1033_0
Fel'shtyn, Alexander; Troitsky, Evgenij. Théorie de Burnside–Frobenius tordue pour les groupes virtuellement polycycliques. Comptes Rendus. Mathématique, Tome 346 (2008) no. 19-20, pp. 1033-1038. doi : 10.1016/j.crma.2008.09.003. http://www.numdam.org/articles/10.1016/j.crma.2008.09.003/
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