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We impose constraints on the topology of the Universe determined from asearch for matched circles in the cosmic microwave background (CMB) temperatureanisotropy patterns of the 7-year WMAP data. We pay special attention to thesensitivity of the method to residual foreground contamination of the sky maps.A search for pairs of matched back-to-back circles in the higher resolutionWMAP W-band map allows tighter constraints to be imposed on topology. Ourresults rule out universes with topologies that predict pairs of such circleswith radii larger than approximately 10 degrees. This places a lower bound onthe size of the fundamental domain for a flat universe of about 27.9 Gpc. Westudy also the possibility for constraining the topology of the Universe bymeans of the matched circles statistic applied to polarised CMB anisotropymaps. The advantages of using the CMB polarisation maps in studies of thetopology over simply analysing the temperature data as has been done to-dateare clearly demonstrated. It is found that the noise levels of both Planck andnext generation CMB experiments data are no longer prohibitive and should below enough to enable the use of the polarisation maps for such studies.

Constraints on the topology of the Universe derived from the 7-year WMAP  CMB data and prospects of constraining the topology using CMB polarisation  maps