An Introduction to Totally Disconnected Locally Compact Groups and Their Finiteness Conditions

We introduce the theory of totally disconnected locally compact (TDLC) groups, including basic properties of topological groups, a proof of van Dantzig’s theorem and some of the most popular (and trouble-free) examples of TDLC groups. The focus is onTDLC groups that satisfy (homological) finiteness conditions with more emphasis on compact generation: for compactly generated TDLC groups, the notion of the Cayley–Abels graph permits us to deal with the topological group as a geometric object.