I will present a procedure that turns certain abstract presentations, such as those for surface groups, Thompson groups, and Artin groups into topological groups with a prescribed open subgroup. These all share some topological properties depending on the chosen open subgroup. For studying cohomological finiteness conditions, we concentrate on totally disconnected locally compact RAAGs and present a generalisation of the Salvetti complex for these groups.

This is joint work with Ilaria Castellano, Bianca Marchionna and Yuri Santos Rego.