Geometry of Reidemeister classes and twisted Burnside theorem

TL;DR

This paper provides an expository overview of Reidemeister classes, twisted Burnside-Frobenius theory, and related properties, discussing their geometric and algebraic aspects with references to recent progress.

Contribution

It offers a comprehensive exposition of Reidemeister classes and twisted Burnside theory, highlighting their geometric and algebraic structures and recent developments.

Findings

Discussion of Reidemeister classes and twisted Burnside theory

Connections to R-infinity property and congruences

Summary of recent progress in the field

Abstract

This is a (mostly expository) paper on Reidemeister classes, twisted Burnside-Frobenius theory, congruences, R-infinity property and all that. It was written in 2005 and published in 2008. We post it as it was, only the bibliography data is updated. For some of the recent progress see e.g. arXiv:0903.4533, arXiv:0903.3455, arXiv:0802.2937, arXiv:0712.2601, arXiv:0704.3411, arXiv:math/0703744, arXiv:math/0606725, arXiv:math/0606764, arXiv:0805.1371 and references there.