Consequences of Observational Uncertainties on the Detection of Cosmic Topology

The observed values of density parameters inevitably involve uncertainties. We study the conditions for detectability and undetectability of cosmic topology in presence of such uncertainties. We present closed analytical forms of (un)detectability conditions for infinite redshift, which are important because: (i) they allow the examine of the detectability of cosmic topology not only for individual manifolds (topologies), but also in whole classes of manifolds; (ii) they are, to a very good approximation, (un)detectibility conditions for z=1100.