Topology beyond the horizon: how far can it be probed?

The standard cosmological model does not determine the spatial topology of the universe. This article revisits the signature of a non-trivial topology on the properties of the cosmic microwave background anisotropies. We show that the correlation function of the coefficients of the expansion of the temperature and polarization anisotropies in spherical harmonics, encodes a topological signature that can be used to distinguish a multi-connected space from an infinite space on sizes larger than the last scattering surface. The effect of the instrumental noise and of a galactic cut are estimated. We thus establish boundaries for the size of the biggest torus dintinguisable with temperature and polarization CMB data. We also describe the imprint of the spatial topology on the 3-point function and on non-Gaussianity.