Twisted Burnside-Frobenius theory for virtually polycyclic groups.

DOI10.1016/j.crma.2008.09.003zbMath1178.20038OpenAlexW1987426822MaRDI QIDQ952115

Alexander Fel'shtyn, Evgenij V. Troitsky

Publication date: 6 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.09.003

zbMATH Keywords

numbers of conjugacy classesautomorphismsirreducible unitary representationstwisted conjugacy classesReidemeister numbersvirtually polycyclic groups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Ordinary representations and characters (20C15) Geometric group theory (20F65) Unitary representations of locally compact groups (22D10) Automorphisms of infinite groups (20E36) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Fundamental group, presentations, free differential calculus (57M05) Induced representations for locally compact groups (22D30)

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New directions in Nielsen-Reidemeister theory

Cites Work

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• Twisted Burnside theorem for type \(\text{II}_1\) groups: an example.
• Small cancellations over relatively hyperbolic groups and embedding theorems.
• The Reidemeister number of any automorphism of a Gromov hyperbolic group is infinite.
• Noncommutative Riesz theorem and weak Burnside type theorem on twisted conjugacy
• Most automorphisms of a hyperbolic group have very simple dynamics
• Trace formulae, Zeta functions, congruences and Reidemeister torsion in Nielsen theory
• TWISTED CONJUGACY CLASSES IN EXPONENTIAL GROWTH GROUPS
• Dynamical zeta functions, Nielsen theory and Reidemeister torsion