Strongly bounded generation in transformation groups

Nick Vlamis (CUNY)

Abstract: Up to quasi-isometry, finitely generated groups admit a canonical left-invariant metric, making large-scale geometric invariants into group-theoretic invariants. Are there other, non-finitely generated abstract groups with this propertyIn this talk, we exhibit such examples by "going against nature"—stripping the topology from several large, rich families of topological transformation groups (e.g., homeomorphism groups of manifolds) and showing that they nevertheless admit canonical large-scale geometries as abstract groups.