Topology of the universegeneral theory of relativity, spacetime is a pseudo-Riemannian manifold. The term topology of the Universe is generally used to mean the 3-manifold of comoving space, even though strictly speaking, it should probably refer only to the underlying topology of this manifold.
We do not yet know the global topology of the Universe, and in fact may never be able to know what it is. However, cosmologistss are trying to measure cosmic topology using data from ground-based and space-based telescopes. Results from the WMAP telescope may give an answer by 2004 or 2005.
The adjective global here means that black holes are ignored - only the properties of space on scales of at least hundreds or thousands of megaparsecs are referred to in the term topology of the Universe.
See also: shape of the Universe, Poincaré conjecture.