2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96500We study the filling invariants at infinity div_{k} for Hadamard manifolds defined by Brady and Farb in [Filling-invariants at infinity for manifolds of nonpositive curvature]. Among other results, we give a positive answer to the question they posed: whether these invariants can be used to detect the rank of a symmetric space of noncompact type.19 pages; New results have been added (section 5). To appear in Geometriae DedicataDifferential Geometry53C35 (Primary) 53C23, 20F67 (Secondary)text