2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74028Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups are exact. We prove this by showing that the group G acts amenably on a compact topological space. We include some applications to the theories of group von Neumann algebras and of measurable orbit equivalence relations.9 pages. Drastically changedGroup TheoryOperator AlgebrasPrimary 20F67; Secondary 46L10, 37A20text