In this paper we investigate finiteness properties of totally disconnected locally compact
groups for general commutative rings R, in particular for R= Z and R= Q. We show these …

This paper is part of the program of studying large-scale geometric properties of totally
disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete …

In several instances, the invariants of compactly generated totally disconnected locally
compact groups acting on locally finite buildings can be conveniently described via …

The main objects of study in this article are pairs (G, H) where G is a topological group with a
compact open subgroup, and H is a finite collection of open subgroups. We develop …

The class of locally compact groups generalises discrete and Lie groups. Locally compact
groups came to light in the first half of the 20th century, and since then they have played a …

It is shown that a Stallings-Swan theorem holds in a totally disconnected locally compact (=
tdlc) context. More precisely, a compactly generated CO-bounded tdlc group of rational …

A 1970 article of J. Tits concerning groups acting on trees introduced an independence
property $(\mathrm {P}) $ as a condition to produce the first examples of nonlinear …

Motivated by the problem of finding a" well-foundedness principle" for totally disconnected,
locally compact (tdlc) groups, we introduce a class $\mathscr {E}^{\mathscr {S}} $ of tdlc …

The class of locally compact groups has been widely studied in group theory, representation
theory, and harmonic analysis. There is a current program of extending geometric …

These are notes of the expository lectures that will be delivered for the LMS Autumn Algebra
School, 21-25 September 2020. The aim is to introduce beginning Ph. D. students to the …