  Recent studies of the detectability of cosmic topology of nearly flat
universes have often concentrated on the range of values of $\Omega_{0}$ given
by current observations. Here we study the consequences of taking the bounds on
$\Omega_{0}$ given by inflationary models, i.e. $|\Omega_0 - 1| \ll 1$. We show
that in this limit, a generic detectable non-flat manifold is locally
indistinguishable from either a cylindrical ($R^2 \times S^1$) or toroidal ($R
\times T^2$) manifold, irrespective of its global shape, with the former being
more likely. Importantly this is compatible with some recent indications based
on the analysis of high resolution CMB data. It also implies that in this limit
an observer would not be able to distinguish topologically whether the universe
is spherical, hyperbolic or flat. By severely restricting the expected
topological signatures of detectable isometries, our results provide an
effective theoretical framework for interpreting cosmological observations, and
can be used to confine any parameter space which realistic search strategies,
such as the `circles in the sky' method, need to concentrate on. This is
particularly important in the inflationary limit, where the precise nature of
cosmic topology becomes undecidable.
