WoG 2023 Talk 2.4: Josiah Oh - Quasi-isometric rigidity of high-dimensional graph manifolds

Speaker: Josiah Oh (Fudan University)

Title: Quasi-isometric rigidity of high-dimensional graph manifolds
Abstract: Frigerio-Lafont-Sisto define a high-dimensional graph manifold to be a manifold that is built from pieces, where each piece is the product of a torus and a finite-volume non-compact hyperbolic manifold of dimension at least 3. They prove that any group quasi-isometric to the fundamental group of a high-dimensional graph manifold must split as the fundamental group of a graph of groups, where the algebraic structure of the vertex and edge groups is determined. In this talk we discuss this theorem, the main ideas in the proof, and work in progress towards a generalization.