Past lectures

Abstract

Group cohomology is an area of mathematics relying on a rich interaction between algebra and topology. In this course we will introduce some important concepts in group cohomology using both algebraic and topological methods. In particular, we shall cover:

- Definition of group cohomology (for discrete groups) via free resolutions (necessary background in homological algebra will be introduced).

- Topological interpretation, group presentations, the presentation-​2-complex, Eilenberg-​Mac Lane spaces

- Cohomological finiteness conditions (for discrete groups): cohomological dimension, groups of type FP, groups of type F, Brown’s criterion

Totally disconnected locally finite (tdlc) groups

- Discrete cohomology for tdlc groups

- Overview of finiteness conditions for tdlc groups

- Classifying spaces for families of subgroups and their finiteness conditions/ Bredon cohomology (for discrete and tdlc groups)