  We study the possibility for constraining the topology of the Universe by
means of the matched circles statistic applied to polarised cosmic microwave
background (CMB) anisotropy maps. The advantages of using the CMB polarisation
maps in studies of the topology over simply analysing the temperature data as
has been done to-date are clearly demonstrated. We test our algorithm to search
for pairs of matched circles on simulated CMB maps for a universe with the
topology of 3-torus. It is found that the noise levels of both Planck and next
generation CMB experiments data are no longer prohibitive and should be low
enough to enable the use of the polarisation maps for such studies. For such
experiments the minimum radius of the back-to-back matched circles which can be
detected are determined. We also showed that the polarisation generated after
reionisation does not have an impact on detectability of the matched circles.
