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Hyperbolic groups with
logarithmic separation profile
Nir Lazarovich and Corentin Le Coz |
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Algebraic & Geometric Topology 25 (2025) 39–54
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Abstract |
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We prove that hyperbolic groups with logarithmic separation profiles split over cyclic groups. This shows that such groups can be inductively built from Fuchsian groups and free groups by amalgamations and HNN extensions over finite or virtually cyclic groups. However, we show that not all groups admitting such a hierarchy have logarithmic separation profile by providing an example of a surface amalgam over a cyclic group with superlogarithmic separation profile. |
Keywords
geometric group theory, hyperbolic groups, asymptotic
properties of groups, coverings, fundamental group
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Mathematical Subject Classification
Primary: 20E06, 20F65, 20F67, 20F69, 51F30
Secondary: 14H30
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References |
Publication
Received: 19 November 2021
Revised: 28 February 2023
Accepted: 1 October 2023
Published: 5 March 2025
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Authors |
| Nir Lazarovich | |
| Department of Mathematics Technion – Israel Institute of Technology Haifa Israel |
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| https://lazarovich.net.technion.ac.il/ | |
| Corentin Le Coz | |
| Department of Mathematics: Algebra
and Geometry (WE01) Ghent University Ghent Belgium |
Oppida Montigny-le-Bretonneux France |
| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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