Strong and uniform boundedness of groups

Jarek Kedra; Assaf Libman; Ben Martin

doi:10.1142/S1793525321500497

Strong and uniform boundedness of groups

Mathematical Science

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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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
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	https://doi.org/10.1142/S1793525321500497
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.

Funding

This work was funded by Leverhulme Trust Research Project Grant RPG-2017-159.

Funders	Funder number
The Leverhulme Trust	RPG-2017-159

Keywords

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

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Kedra_etal_JTA_Strong_And_Uniform_AAM
Electronic version of an article published as [Journal of Topology and Analysis, Volume, Issue, Year, Pages] [Article DOI] © [copyright World Scientific Publishing Company] [Journal URL]
Accepted author manuscript, 564 KBLicence: Unspecified

Cite this

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keywords = "Bounded group, conjugation-invariant norm, lattice, Lie group, linear algebraic groups, symplectic manifold, quasimorphism",

author = "Jarek Kedra and Assaf Libman and Ben Martin",

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KW - Bounded group

KW - conjugation-invariant norm

KW - lattice

KW - Lie group

KW - linear algebraic groups

KW - symplectic manifold

KW - quasimorphism

U2 - 10.1142/S1793525321500497

DO - 10.1142/S1793525321500497

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JF - Journal of Topology and Analysis

IS - 3

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Strong and uniform boundedness of groups

Abstract

Bibliographical note

Funding

Keywords

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