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
Pages (from-to)707-739
Number of pages37
JournalJournal of Topology and Analysis
Issue number3
Early online date24 Sept 2021
Publication statusPublished - 1 Sept 2023

Bibliographical note

Acknowledgements. We thank Philip Dowerk, Światosław Gal, Étienne Ghys, Vincent Humilière, Morimichi Kawasaki, Nicolas Monod, Dave Morris, Leonid Polterovich and Yehuda Shalom for helpful comments and for answering our questions. This work was funded by Leverhulme Trust Research Project Grant RPG-2017-159.


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


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