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.
Original language | English |
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Pages (from-to) | 707-739 |
Number of pages | 37 |
Journal | Journal of Topology and Analysis |
Volume | 15 |
Issue number | 3 |
Early online date | 24 Sept 2021 |
DOIs | |
Publication status | Published - 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.Keywords
- Bounded group
- conjugation-invariant norm
- lattice
- Lie group
- linear algebraic groups
- symplectic manifold
- quasimorphism