Geometry of Reidemeister classes and twisted Burnside theorem

DOI10.1017/is008001006jkt028zbMath1215.22003arXiv0909.1710OpenAlexW3100184137MaRDI QIDQ3549298

Evgenij V. Troitsky, Alexander Fel'shtyn

Publication date: 22 December 2008

Published in: Journal of K-theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1710

zbMATH Keywords

\(C^*\)-algebraunitary representationsFourier-Stieltjes algebratwisted conjugacy classesReidemeister numberBurnside theorem

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Unitary representations of locally compact groups (22D10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Fixed points and coincidences in algebraic topology (55M20) Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. (43A30)

Related Items (11)

Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups ⋮ Twisted conjugacy classes of the unit element. ⋮ The twisted commutator subgroups and questions of Fel'shtyn and Troitsky ⋮ Twisted conjugacy classes in nilpotent groups. ⋮ New zeta functions of Reidemeister type and the twisted Burnside-Frobenius theory ⋮ Reidemeister classes and twisted inner representations. ⋮ The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups. ⋮ New directions in Nielsen-Reidemeister theory ⋮ The Nielsen and Reidemeister numbers of maps on infra-solvmanifolds of type \((\mathrm{R})\) ⋮ Reidemeister classes in lamplighter-type groups ⋮ Dold sequences, periodic points, and dynamics

Cites Work

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• The structure of algebras of operator fields
• Twisted Burnside theorem for type \(\text{II}_1\) groups: an example.
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• The Selberg-Arthur trace formula. Based on lectures by James Arthur
• The Reidemeister zeta function with applications to Nielsen theory and a connection with Reidemeister torsion
• On the asymptotic geometry of Abelian-by-cyclic groups
• Über unitäre Darstellungen abzählbarer, diskreter Gruppen
• Lectures on Nielsen fixed point theory
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• TWISTED CONJUGACY CLASSES IN EXPONENTIAL GROWTH GROUPS
• Embedding Theorems for Groups
• Groups with Finite Classes of Conjugate Elements (In Memoriam Issai Schur)

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