Finitely generated groups acting uniformly properly on hyperbolic space

Robert Kropholler; Vladimir Vankov

doi:10.4171/GGD/659

Finitely generated groups acting uniformly properly on hyperbolic space

Robert Kropholler, Vladimir Vankov

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on hyperbolic spaces that are not virtually torsion-free and cannot be subgroups of hyperbolic groups.

Original language	English
Pages (from-to)	101-109
Number of pages	9
Journal	Groups, Geometry, and Dynamics
Volume	17
Issue number	1
DOIs	https://doi.org/10.4171/GGD/659
Publication status	Published - 27 Jan 2023

Bibliographical note

Publisher Copyright:
© 2023 European Mathematical Society.

Keywords

hyperbolic space
not virtually torsion-free
Uniformly proper action

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10.4171/GGD/659Licence: CC BY

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title = "Finitely generated groups acting uniformly properly on hyperbolic space",

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AU - Vankov, Vladimir

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AB - We construct an uncountable sequence of groups acting uniformly properly on hyperbolic spaces. We show that only countably many of these groups can be virtually torsion-free. This gives new examples of groups acting uniformly properly on hyperbolic spaces that are not virtually torsion-free and cannot be subgroups of hyperbolic groups.

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KW - not virtually torsion-free

KW - Uniformly proper action

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DO - 10.4171/GGD/659

M3 - Article (Academic Journal)

AN - SCOPUS:85151133521

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JO - Groups, Geometry, and Dynamics

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Finitely generated groups acting uniformly properly on hyperbolic space

Abstract

Bibliographical note

Keywords

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