240153 Introduction to locally compact groups (VÜA) (SoSe 2026)

The lecture provides an introduction into the structure theory of locally compact groups. Locally compact groups are, for example, matrix group like GL(n,R), but also automorphism groups of certain graphs. We will see how to split up a locally compact groups into a connected group and a totally disconnected group, and how each of these can be studied.
Here is the planned outline:

Topological groups
Classification of local fields
Lie groups over local fields
The Haar measure
Connected groups and the Gleason-Yamabe theorem
Totally disconnected, locally compact groups

Requirements for participation, required level

Basic group theory, basic point set topology