Topological lensing in spherical spaces

This paper gives the construction and complete classification of all three-dimensional spherical manifolds and orders them by decreasing volume, in the context of multi-connected universe models with positive spatial curvature. It discusses which spherical topologies are likely to be detectable by crystallographic methods using three-dimensional catalogues of cosmic objects. The expected form of the pair separation histogram is predicted (including the location and height of the spikes) and is compared to computer simulations, showing that this method is stable with respect to observational uncertainties and is well suited for detecting spherical topologies.