AG Lie-Gruppen: C. Bönicke, Newcastle University: Homology of étale groupoids and applications

Homology of étale groupoids and applications – Vortragender: Christian
Bönicke, Newcastle University (UK) – Einladender: Kang Li

Abstract: The aim of these lectures is to give a gentle introduction to a
homology theory for étale groupoids first developed by Crainic and Moerdijk in
2000. This theory has recently attracted a lot of attention from the operator
algebras and topological dynamics communities. Applications in these areas
largely deal with totally disconnected étale groupoids and hence we will also
be focussing on this setting.

My plan is to first introduce étale groupoids and give a number of examples
from different contexts. We will then turn to the definition of groupoid
homology, develop some useful tools, and treat some of the examples from
before in more detail. Finally, we will discuss how groupoid homology relates
to operator algebras, topological dynamics, and group theory.