Integral Measure Equivalence versus Quasi-Isometry for Right-Angled Artin Groups

Explore the relationship between integral measure equivalence and quasi-isometry for right-angled Artin groups in this hour-long lecture from the Workshop on Cube Complexes and Combinatorial Geometry. Delve into the topological definition of quasi-isometry proposed by Gromov and its measure-theoretic analogue, measure equivalence. Examine similarities between quasi-isometric invariants and measure equivalence invariants for cubical groups. Focus on right-angled Artin groups, discovering how a countable group with bounded torsion that is integrable measure equivalent to a right-angled Artin group with finite outer automorphism group must be finitely generated and quasi-isometric to it. Learn about the groundbreaking approach of deducing integrable measure equivalence rigidity results from quasi-isometric rigidity results for a wide class of right-angled Artin groups, marking one of the first instances where quasi-isometry establishes a rigidity result in measure equivalence.