Exploring the global topology of the universe

We review the work done by our group on cosmic topology. It ranges from early atempts to solve a famous controversy about quasars thought the multiplicity of images, to quantum cosmology in this context and an application to QED renormalization.

A SUGGESTION ON THE PAIR OF QSO TRIPLETS 1130+106 (B,A,C), (X,Y,Z)

The alignment of a pair of QSO triplets discovered by Arp and Hazard are tentatively explained by a combination of (I) the idea of quasar ejection by galaxies; (II) a construction by Narlikar suggesting a common origin for the six images; and (III) a nontrivial topology of cosmic space.

SMALLEST UNIVERSE OF NEGATIVE CURVATURE

The smallest known three-dimensional closed manifold of curvature k = -1 was discovered a few years ago by Weeks. This kind of manifold is constructed from a hyperbolic polyhedron with faces pair-wise identified. Here it is used as the comoving spatial section of a Friedmann cosmological model, in the spirit of Ellis and Schreiber's idea of small universes. Its nontrivial global topology has the effect of producing multiple images of single cosmic sources, and this is the basis of an attempt to solve a famous controversy about the redshifts of quasars.