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arXiv · 2110.13595

Hyperbolic groups with logarithmic separation profile

Nir Lazarovich·Corentin Le Coz
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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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Nir Lazarovich, Corentin Le Coz. 2021-10-26. Hyperbolic groups with logarithmic separation profile. https://doi.org/10.2140/agt.2025.25.39

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