Right-angled Artin groups (RAAGs) are defined from a simplicial graph by taking one generator for each vertex and imposing that two generators commute exactly when the corresponding vertices are joined by an edge. They form a rich class of groups interpolating between free groups and free abelian groups. In ongoing joint work with Shaked Bader and Harry Petyt, we study quasi-isometric embeddings between RAAGs and show that they display both rigidity and flexibility phenomena.

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