Abstract

Classifying spaces for families of subgroups have been widely studied in the case of the families of finite subgroups and virtually cyclic subgroups, due to them being the geometrical objects in the Baum-Connes Conjecture and Farrell-Jones Conjecture, respectively. However, those definitions and the Bredon Cohomology on which the algebraic meaning of this objects relies are stated for all families of subgroups. For that reason, classifying spaces for larger families of subgroups is a hardly explored and rich field. The aim of this talk is to define and illustrate with some examples and properties the concept of classifying spaces for families of subgroups and present a piece of my work on such spaces. In particular, I will explain the construction of models for the classifying space for the family of subgroups of a polycyclic group $G$ of Hirsch length less than or equal to $r$.

Please note: the seminar is in a different room and at a different time than usual, because it is joint with the Junior Geometry Seminar, see here.