  An important, and potentially detectable, signature of a non-trivial topology
for the universe is the presence of so called circles-in-the-sky in the cosmic
microwave background (CMB). Recent searches, confined to antipodal and nearly
antipodal circles, have however failed to detect any. This outcome, coupled
with recent theoretical results concerning the detectability of very nearly
flat universes, is sufficient to exclude a detectable non-trivial cosmic
topology for most observers in the inflationary limit ($0< |\Omega_{tot}-1|
\lesssim 10^{-5}$). In a recent paper we have studied the consequences of these
searches for circles if the Universe turns out to be exactly flat
($\Omega_{tot} = 1 $) as is often assumed. More specifically, we have derived
the maximum angles of deviation possible from antipodicity of pairs of matching
circles associated with the shortest closed geodesic for all multiply-connected
flat orientable $3$-manifolds. These upper bounds on the deviation from
antipodicity demonstrate that in a flat universe for some classes of topology
there remains a substantial fraction of observers for whom the deviation from
antipodicity of the matching circles is considerably larger than zero, which
implies that the searches for circles-in-the-sky undertaken so far are not
enough to exclude the possibility of a detectable non-trivial flat topology.
Here we briefly review these results and discuss their consequences in the
search for circles-in-the-sky in a flat universes.
