Embeddings between square-free right-angled Artin groups
by
B/2nd floor-B.203 - Seminar room
Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve)
Right-angled Artin groups (RAAGs) are a natural class of examples in geometric group theory. These groups have a finite presentation where every relator is the commutator of two generators, which can be encoded by a graph. A result of Droms states that two 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 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.