2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75602In this paper we define two regular homotopy invariants c and i for immersions of oriented 3-manifolds into R^5 in a geometric manner. The pair (c(f),i(f)) completely describes the regular homotopy class of the immersion f. The invariant i corresponds to the 3-dimensional obstruction that arises from Hirsch-Smale theory and extends the one defined in [10] for immersions with trivial normal bundle.17 pagesGeometric TopologyAlgebraic Topology57N35; 57R45; 57R42text