Key points are not available for this paper at this time.
We show that if H H is a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G G , then H H is virtually a free product of hyperbolic surface groups and free groups. We prove that whenever a one-ended hyperbolic group H H is a fiber of a non-trivial hyperbolic bundle then H H virtually splits over a 2-ended subgroup.
Lazarovich et al. (Sat,) studied this question.