Strong and uniform boundedness of groups

Abstract

A group G is called bounded if every conjugation-invariant norm on G has finite diameter. We introduce various strengthenings of this property and investigate them in several classes of groups including semisimple Lie groups, arithmetic groups and linear algebraic groups. We provide applications to Hamiltonian dynamics.

28 pages; revised version; accepted in Journal of Topology and Analysis

References in corpus (3)

• Uniform symplicity of groups with proximal action
• Strong distortion in transformation groups
• Strong approximation methods in group theory, an LMS/EPSRC Short course lecture notes

Cited by in corpus (1)

• Commuting symplectomorphisms on a surface and the flux homomorphism