hi everyone on cos-top,
The Ulm group continue to work on T^3 models - here's a nice new paper:
http://arXiv.org/abs/0903.3133
Other news: there's an observational signature of cosmic topology which occurs for flat compact models but not for curved compact models (assuming standard physical components of the Universe in both cases).
The good news for cosmic topology in general: this observational signature has been detected to extremely high significance! :)
The bad news for the Poincare space: this observational signature has been detected to extremely high significance! :(
Details: http://arxiv.org/abs/0904.0975
A Poincare space is certainly not excluded by the argument, but it would require an exotic explanation for the observational signature rather than a simple explanation. Occam's razor suggests that we may have to accept T^3 (or another flat compact space).
Anyway, see the paper to find out what this observational signature is.
cheers boud