Group theoretic conditions under which closed aspherical manifolds are covered by Euclidean space

Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we will prove variations of this theorem in all dimensions by presenting conditions on finitely presented groups that guarantee simple connectivity at infinity. The proofs that we give will all be geometric.