Topological RAAGs
by
B/2nd floor-B.203 - Seminar room
Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve)
Right-angled Artin groups (RAAGs) form a family of finitely generated groups that play an important role in geometric and computational group theory. Their study is often related to the one of their universal Salvetti complex, a CAT(0)-cube complex on which they act geometrically.
In this talk, we introduce a generalisation of RAAGs to topological groups based on the notion of generalised presentations. Remarkably, those groups have a cellular action on a thicker version of the universal Salvetti complex of a RAAG with controlled cell stabilisers. Due to the high connectivity of this complex, we can deduce homological/homotopical finiteness properties for topological RAAGs. On the way, we will also discuss the connection of this complex with Cayley-Abels graphs of the relevant groups, and describe a canonical building-like structure on it.
Work in progress with I. Castellano, B. Nucinkis, and Y. Santos Rego.