Séance Séminaire

Séminaire Gaston Darboux

Quasi-isometric embeddings of Right-angled Artin groups

A right-angled Artin group (RAAG) is obtained from a finite graph by assigning a generator to each vertex and declaring that two generators commute exactly when their vertices are joined by an edge. Quasi-isometries between RAAGs have been extensively studied and exhibit striking rigidity. In a joint work with Shaked Bader and Harry Petyt, we turn to quasi-isometric embeddings and show that, in many cases, any such embedding between two RAAGs forces explicit combinatorial constraints on their defining graphs. The techniques we develop allow us to recover rigidity results for quasi-isometric embeddings between symmetric spaces and Euclidean buildings.