2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64177We discuss the relationship between the m-th homotopy group of the one-point union of r copies of the two-dimensional sphere and the m-th homotopy group of the one-point union of r+1 copies of the Thom space of the oriented two-dimensional universal vector bundle. Using a suitably choosen isomorphism between them a forgetful homomorphism is computed by evaluating on factors of the Hilton splitting.5 figures; revised on 6 JuneGeometric TopologyAlgebraic Topology55Q20;57Q45text