Finiteness properties of totally disconnected locally compact groups

Abstract

In this paper we investigate finiteness properties of totally disconnected locally compact groups for general commutative rings $R$, in particular for $R=\mathbb{Z}$ and $R=\mathbb{Q}$. We show these properties satisfy many analogous results to the case of discrete groups, and we provide analogues of the famous Bieri's and Brown's criteria for finiteness properties and deduce that both $F{P}_n$-properties and $F_n$-properties are quasi-isometric invariant. Moreover, we introduce graph-wreath products in the category of totally disconnected locally compact groups and discuss their finiteness properties.

References in corpus (8)

• Metric geometry of locally compact groups
• Finitely presented wreath products and double coset decompositions
• The Brin-Thompson groups sV are of type F_\infty
• Locally compact wreath products
• Homological finiteness properties of wreath products
• Rational discrete cohomology for totally disconnected locally compact groups
• Graphs, permutations and topological groups
• Homotopical Algebra in Categories with Enough Projectives

Cited by in corpus (2)

• Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups
• On homological properties of the Schlichting completion