Embeddings between square-free right-angled Artin groups

by Adrien Abgrall (École Normale Supérieure de Lyon)

Friday Nov 6, 2026, 3:00 PM → 4:00 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

A result of Droms states that two right-angled Artin groups (RAAGs) are isomorphic if and only if their defining graphs are isomorphic. However, deciding whether one RAAG embeds as a subgroup of another is a much harder, and largely open, problem. Substantial progress was made by Kim and Koberda, notably solving the two-dimensional case, relying on their definition of the extension graph of a RAAG, an object somewhat analogous to the curve graph of a surface. Quasi-isometric embedding between RAAGs was also recently studied by Bader–Bensaïd–Petyt. I will present a joint work with Sasha Gurieva and Camille Horbez where we investigate measurable embedding, a measured analogue of coarse embedding. We completely characterize measurable embedding among square-free RAAGs (i.e. RAAGs that do not contain F2 x F2). Interestingly, the characterization is both in terms of subgroup embedding and of extension graphs. It is also algorithmically decidable.

Geometry and Groups in North Rhine-Westphalia