2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74877A standard fact about two incompressible surfaces in an irreducible 3-manifold is that one can move one of them by isotopy so that their intersection becomes $π_1$-injective. By extending it on the maps of some 3-dimensional $\mathbb{Z}_n$-manifolds into 4-manifolds, we prove that any homotopy equivalence of 4-dimensional graph-manifolds with reduced graph-structures is homotopic to a diffeomorphism preserving the structures. Keywords: graph-manifold, $π_1$-injective $\mathbb{Z}_n$-submanifold.8 pages, 11 figuresGeometric Topologytext