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We reexamine the possibility of the detection of the cosmic topology innearly flat hyperbolic Friedmann-Lemaitre-Robertson-Walker (FLRW) universes byusing patterns repetition. We update and extend our recent results in twoimportant ways: by employing recent observational constraints on thecosmological density parameters as well as the recent mathematical resultsconcerning small hyperbolic 3-manifolds. This produces new bounds withconsequences for the detectability of the cosmic topology. In addition toobtaining new bounds, we also give a concrete example of the sensitivedependence of detectability of cosmic topology on the uncertainties in theobservational values of the density parameters.Comment: 10 pages, 2 figures, LaTeX2e. To appear in Int. J. Mod. Phys. A  (2002). Contribution to the Fifth Alexander Friedmann International Seminar  on Gravitation and Cosmolog

LIMITS ON THE DETECTABILITY OF COSMIC TOPOLOGY IN HYPERBOLIC UNIVERSES