The topology of the universe: the biggest manifold of them all

Clues as to the geometry of the universe are encoded in the cosmic background radiation. Hot and cold spots in the primordial radiation may be randomly distributed in an infinite universe while in a universe with compact topology distinctive patterns can be generated. With improved vision, we could actually see whether the universe is wrapped into a hexagonal prism or a hyperbolic horn. We discuss the search for such geometric patterns in predictive maps of the microwave sky.