2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63008We consider the following properties of compact oriented irreducible graph-manifolds: to contain a $π_1$-injective surface (immersed, virtually embedded or embedded), be (virtually) fibered over $S^1$, and to carry a metric of nonpositive sectional curvature. It turns out that all these properties can be described from a unified point of view.17 pagesGeometric Topology57M50 (Primary) 57M10, 57N10, 57N35 (Secondary)text