Limits of crystallographic methods for detecting space topology

We investigate to what extent the cosmic crystallographic methods aimed to detect the topology of the universe using catalogues of cosmic objects would be damaged by various observational uncertainties. We find that the topological signature is robust in the case of Euclidean spaces, but is very fragile in the case of compact hyperbolic spaces. Comparing our results to the presently accepted range of values for the curvature parameters, the best hopes for detecting space topology rest on elliptical space models.