Chennai Mathematical Institute


Date: Tuesday, August 10, 2021.
Time: 3:30 PM.
Soluble matrix groups and twisted conjugacy classes

Yuri Santos Rego
Otto-von-Guericke Universit├Ąt Magdeburg.


Several authors have investigated twisted conjugacy classes for linear groups. As it turns out, all known examples which happen to be nonamenable, such as lattices in simple Lie groups, exhibit the so-called property R_\infty, which says that all automorphisms of the given group have infinitely many twisted conjugacy classes. In contrast, several families of soluble linear groups contain members that do and members that do not have R_\infty, making the soluble case rather mysterious. In this talk we will discuss the current state of knowledge regarding Reidemeister numbers of (soluble) matrix groups, with S-arithmetic groups serving as chief examples. This is based on joint work with Paula M. Lins de Araujo (KU Leuven Kulak, Belgium).