2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71250Given an irreducible contractible open 3-manifold W which is not homeomorphic to R^3, there is an associated simplicial complex S(W), the complex of end reductions of W. Whenever W covers a 3-manifold M one has that the fundamental group of M is isomorphic to a subgroup of the group Aut(S(W)) of simplicial automorphisms of W. In this paper we give a new method for constructing examples W with S(W) isomorphic to a triangulation of R. It follows that any 3-manifold M covered by W must have infinite cyclic fundamental group. We also give a complete isotopy classification of the end reductions of W.23 pages, 3 figures, to appear in Boletin de la Sociedad Matematica Mexicana special issue (Ficofest Proceedings) in honor of Francisco Gonzalez-AcunaGeometric Topologytext