Geodesic
Hyperbolic groups with logarithmic separation profile
Lazarovich, Nir1 ; Le Coz, Corentin2
1Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel
2Department of Mathematics: Algebra and Geometry (WE01), Ghent University, Ghent, Belgium, Oppida, Montigny-le-Bretonneux, France
Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 39-54
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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.

DOI : 10.2140/agt.2025.25.39
Keywords: geometric group theory, hyperbolic groups, asymptotic properties of groups, coverings, fundamental group

Lazarovich, Nir  1   ; Le Coz, Corentin  2

1 Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel
2 Department of Mathematics: Algebra and Geometry (WE01), Ghent University, Ghent, Belgium, Oppida, Montigny-le-Bretonneux, France 
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Lazarovich, Nir; Le Coz, Corentin. Hyperbolic groups with logarithmic separation profile. Algebraic and Geometric Topology, Tome 25 (2025) no. 1, pp. 39-54. doi: 10.2140/agt.2025.25.39

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