Strong and uniform boundedness of groups

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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.
Original languageEnglish
JournalJournal of Topology and Analysis
Early online date24 Sep 2021
Publication statusE-pub ahead of print - 24 Sep 2021


  • Bounded group
  • conjugation-invariant norm
  • lattice
  • Lie group
  • linear algebraic groups
  • symplectic manifold
  • quasimorphism


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