  It is shown here how prior estimates on the local shape of the universe can
be used to reduce, to a small region, the full parameter space for the search
of circles in the sky. This is the first step towards the development of
efficient estrategies to look for these matched circles in order to detect a
possible nontrivial topology of our Universe. It is shown how to calculate the
unique point, in the parameter space, representing a pair of matched circles
corresponding to a given isometry $g$ (and its inverse). As a consequence, (i)
given some fine estimates of the covering group $\Gamma$ of the spatial section
of our universe, it is possible to confine, in a very effective way, the region
of the parameter space in which to perform the searches for matched circles,
and reciprocally (ii) once identified such pairs of matched circles, one could
determine with greater precision the topology of our Universe and our location
within it.
