Commensurated hyperbolic subgroups

2023/09/24 by Lazarovich, Nir, Margolis, Alex, Mj, Mahan
#20F65 #20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2309.13644

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.

Related

• Hyperbolic groups that are not commensurably coHopfian
• Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups
• Commensurability and locally free Kleinian groups
• Surface groups among cubulated hyperbolic and one-relator groups
• The geometry of surface-by-free groups