Commensurated hyperbolic subgroups

Lazarovich, Nir; Margolis, Alex; Mj, Mahan

doi:10.1090/tran/9209

Commensurated hyperbolic subgroups
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by Nir Lazarovich, Alex Margolis and Mahan Mj;

Trans. Amer. Math. Soc. 377 (2024), 7377-7402

DOI: https://doi.org/10.1090/tran/9209

Published electronically: July 19, 2024

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Abstract:

We show that if $H$ is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group $G$, then $H$ is virtually a free product of hyperbolic surface groups and free groups. We prove that whenever a one-ended hyperbolic group $H$ is a fiber of a non-trivial hyperbolic bundle then $H$ virtually splits over a 2-ended subgroup.

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