New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory

DOI10.1134/S1061920820020065zbMath1443.37025arXiv1804.02874OpenAlexW3032013842MaRDI QIDQ2187316

M. Ziętek, Alexander Fel'shtyn, Evgenij V. Troitsky

Publication date: 2 June 2020

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02874

zbMATH Keywords

zeta functionsendomorphismReidemeister numbersGauss congruences

Mathematics Subject Classification ID

Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30) Automorphisms and endomorphisms of algebraic structures (08A35) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (3)

Pólya-Carlson dichotomy for dynamical zeta functions and a twisted Burnside-Frobenius theorem ⋮ Pólya-Carlson dichotomy for coincidence Reidemeister zeta functions via profinite completions ⋮ Reidemeister classes, wreath products, and solvability

Cites Work

• Unnamed Item
• Unnamed Item
• The \(R_\infty\) and \(S_\infty\) properties for linear algebraic groups
• Sigma theory and twisted conjugacy classes.
• Twisted conjugacy classes in nilpotent groups.
• Twisted conjugacy classes in lattices in semisimple Lie groups
• Twisted Burnside theorem for type \(\text{II}_1\) groups: an example.
• Aspects of the property \(R_\infty\).
• Reidemeister classes and twisted inner representations.
• Twisted conjugacy classes in saturated weakly branch groups.
• Small cancellations over relatively hyperbolic groups and embedding theorems.
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups
• Reidemeister classes in some weakly branch groups
• Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy
• The \(R_\infty\) property for crystallographic groups of Sol
• Most automorphisms of a hyperbolic group have very simple dynamics
• Geometry of Reidemeister classes and twisted Burnside theorem
• Twisted conjugacy classes in nilpotent groups
• Trace formulae, Zeta functions, congruences and Reidemeister torsion in Nielsen theory
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion
• Reidemeister zeta functions of low-dimensional almost-crystallographic groups are rational
• Dynamical zeta functions
• Reidemeister classes in lamplighter-type groups
• Twisted Burnside-Frobenius theory for discrete groups
• The R _∞ property for free groups, free nilpotent groups and free solvable groups
• Profinite Groups

This page was built for publication: New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory