###
Hyperbolic commensurated subgroups

####
Mahan Mj (TIFR)

Abstract: Commensurated subgroups generalize normal subgroups. Let H be a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G. We show that H is virtually a free product of hyperbolic surface groups and free groups. When H is genuinely a normal subgroup, this follows from deep work
of Bestvina, Paulin, Rips, Sela. But when H is only commensurated, we need new
techniques. We also describe restrictions on the electrified graph obtained by electrifying cosets of H. This is joint work with Nir Lazarovich and Alex Margolis.