The study of topology of the universe using multipole vectors
  We study a multipole vector-based decomposition of cosmic microwave background (CMB) data in order to search for signatures of a multiconnected topology of the universe. Using 10^6 simulated maps, we analyse the multipole vector distribution on the sky for the lowest order multipoles together with the probability distribution function of statistics based on the sum of the dot products of the multipole vectors for both the simply-connected flat universe and universes with the topology of a 3-torus. The estimated probabilities of obtaining lower values for these statistics as compared to the 5-year WMAP data indicate that the observed alignment of the quadrupole and octopole is statistically favoured in a 3-torus topology where at least one dimension of the fundamental domain is significantly shorter than the diameter of the observable universe, as compared to the usual standard simply-connected universe. However, none of the obtained results are able to clearly rule out the latter (at more than 97% confidence level). Multipole vector statistics do not appear to be very sensitive to the signatures of a 3-torus topology if the shorter dimension of the domain becomes comparable to the diameter of the observable universe. Unfortunately, the signatures are also significantly diluted by the integrated Sachs-Wolfe effect. 
P. Bielewicz, A. Riazuelo