Three-dimensional Topology-Independent Methods to Look for Global Topology

The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of particle horizon radius) could contain several images of the single, physical Universe. Recent three-dimensional techniques for constraining and/or detecting this topology are reviewed. Initial applications of these techniques using X-ray bright clusters of galaxies and quasars imply (weak) candidates for a non-trivial topology.