Abstract

General relativity theory admits cosmological solutions with multiply-connected space topology, called « wraparound universes ».
First I shall give an overview on the mathemtatical properties of such spaces, on their classification and their visualization (I'll provide 3D stereoscopic glasses).
Next I shall review the observational status of wraparound universes. Cosmic topolgy provides various experimental signatures, the most promising being the full-sky Cosmic Microwave Background (CMB) data. The most recent ones (from the WMAP telescope) are
compatible with a family of « well-proportioned » wraparound universes, including the Poincaré dodecahedral spherical space as the most convincing candidate. In such a model, physical space would be slightly smaller than the observable space ; as a consequence, multiple images of light sources should be expected due to a topological lensing effect. I shall describe the
expected patterns in the CMB sky, discuss what was really found in the WMAP data and the controversies about their interpretation.