On the realizable topology of a manifold with attractors of geodesics

We discuss the so-called realizable topology of a Riemannian manifold with attractors of geodesics, which we understand as its topological properties, mainly that related to its fundamental group, investigated from a viewpoint that may be considered realizable in a sense. In the special approach in which the manifold is understood as a model physical universe, we conclude that its realizable fundamental group is isomorphic to the classical fundamental group of its observable portion. For a universe of dimension at least three whose unobservable components are all contractible, this conclusion ensures the possibility to get real inferences about its classical fundamental group through observational methods.