  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.
