Algèbre
Théorie de Burnside–Frobenius tordue pour les groupes virtuellement polycycliques
[Twisted Burnside–Frobenius theory for virtually polycyclic groups]
Comptes Rendus. Mathématique, Volume 346 (2008) no. 19-20, pp. 1033-1038.

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 ϕˆ 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.

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 ϕˆ 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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.09.003
Fel'shtyn, Alexander 1; Troitsky, Evgenij 2

1 Instytut Matematyki, Uniwersytet Szczecinski, ul. Wielkopolska 15, 70-451 Szczecin, Poland
2 Department of Mechanics and Mathematics, Moscow State University, 119992 GSP-2 Moscow, Russia
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Fel'shtyn, Alexander; Troitsky, Evgenij. Théorie de Burnside–Frobenius tordue pour les groupes virtuellement polycycliques. Comptes Rendus. Mathématique, Volume 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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