Foldings in relatively hyperbolic groups (2403.17686v1)

Abstract: Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is introduced and finiteness results for subgroups of locally relatively quasiconvex relatively hyperbolic groups and Kleinian groups are established.