Journal article

Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Abstract:: We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the associated hyperbolic spaces. We then use quasimorphisms to produce examples where these latter results are sharp.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Abbott, C., Hagen, M., Petyt, H., & Zalloum, A. (2025). Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups. Analysis and Geometry in Metric Spaces, 13(1).

MLA Style

Abbott, C, et al. “Uniform Undistortion from Barycentres, and Applications to Hierarchically Hyperbolic Groups.” Analysis and Geometry in Metric Spaces, vol. 13, no. 1, 2025.

Chicago Style

Abbott, C, M Hagen, H Petyt, and A Zalloum. 2025. “Uniform Undistortion from Barycentres, and Applications to Hierarchically Hyperbolic Groups.” Analysis and Geometry in Metric Spaces 13 (1).
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Files:: Abbott_et_al_2025_Uniform_undistortion_from.pdf

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Publisher copy:: 10.1515/agms-2025-0027

Authors

+ Abbott, C More by this author

Role:: Author

+ Hagen, M More by this author

Role:: Author

+ Petyt, H More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Zalloum, A More by this author

Role:: Author

Publisher:: De Gruyter
Journal:: Analysis and Geometry in Metric Spaces More from this journal
Volume:: 13
Issue:: 1
Article number:: 20250027
Publication date:: 2025-11-26
Acceptance date:: 2025-06-04
DOI:: 10.1515/agms-2025-0027
EISSN:: 2299-3274
ISSN:: 2299-3274

Language:: English
Keywords:: translation length

20F65

51F30

undistorted

hierarchical hyperbolicity

central extension

20F67

injective space
Pubs id:: 2350340
UUID:: uuid_8c871293-f78c-4248-a7a7-7e47292fed1f
Local pid:: pubs:2350340
Source identifiers:: 3510930
Deposit date:: 2025-11-26
ARK identifier:: ark:/29072/ora_8c871293f78c4248a7a77e47292fed1f

Terms of use

Copyright date:: 2025

Licence:: CC Attribution (CC BY)

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