Several analyses of the cosmic microwave background map made by the satellite
WMAP suggest that the global shape of a spatial section of the Universe is that
of a Poincare dodecahedral space. A summary of some of these analyses and a
description of independent tests which should be able to either increase
confidence in the hypothesis or else refute it to extremely high significance
will be presented.Comment: v1 submitted to Proceedings of the Albert Einstein Century
International Conference, held in Paris, France, July 18-22, 2005 - after it
is published, it will be found at http://proceedings.aip.org/proceedings/, v2
has minor correction to one referenc
