Hyperbolic groups with logarithmic separation profile

Nir Lazarovich; Corentin Le Coz

doi:10.2140/agt.2025.25.39

Hyperbolic groups with logarithmic separation profile

Nir Lazarovich, Corentin Le Coz

Mathematics

Technion - Israel Institute of Technology

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

Abstract

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.

Original language	English
Pages (from-to)	39-54
Number of pages	16
Journal	Algebraic and Geometric Topology
Volume	25
Issue number	1
DOIs	https://doi.org/10.2140/agt.2025.25.39
State	Published - 2025

Keywords

asymptotic properties of groups
coverings
fundamental group
geometric group theory
hyperbolic groups

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.2140/agt.2025.25.39

Cite this

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abstract = "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.",

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AB - 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.

KW - asymptotic properties of groups

KW - coverings

KW - fundamental group

KW - geometric group theory

KW - hyperbolic groups

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DO - 10.2140/agt.2025.25.39

M3 - مقالة

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JO - Algebraic and Geometric Topology

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Hyperbolic groups with logarithmic separation profile

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

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