2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112858We describe a natural isomorphism between the set of equivalence classes of pseudocycles and the integral homology groups of a smooth manifold. Our arguments generalize to settings well-suited for applications in enumerative algebraic geometry and for construction of the virtual fundamental class in the Gromov-Witten theory.28 pages, 2 figures; a long technical construction has been simplifiedAlgebraic TopologySymplectic Geometry55N99, 57R95text