2006/06/08 by Alexander Fel’shtyn, Fel'shtyn, Alexander, Evgenij Troitsky +1
Mathematics · #20Cxx #20E45 #22D10 #22D25 #37C25 #43A30 #46Lxx #54H25 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Operator Algebras (math.OA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.math/0606179
openalex publication_date 2006/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finite-dimensional fixed points of the induced map f^ on the unitary dual, if one of these numbers is finite. This theorem is a natural generalization of the classical Burnside-Frobenius theorem to infinite groups. This theorem also has important consequences in topological dynamics and in some sense is a reply to a remark of J.-P. Serre. The main technical results proved in the paper yield a tool for a further progress.