Topology of the Universe: Background and recent observational approaches

Is the Universe (a spatial section thereof) finite or infinite? Knowing the global geometry of a Friedmann-Lemaitre (FL) universe requires knowing bot h its curvature and its topology. A Bat or hyperbolic ('open') FL universe is not necessarily infinite in volume. Multiply connected flat and hyperbolic models are, in general, as consisten t with present observations on scales of 1-20 h(-1)Gpc as are the correspon ding simply connected hat and hyperbolic models. The methods of detecting m ultiply connected models (MCM's) are presently in their pioneering phase of development and the optimal observationally realistic strategy is probably yet to be calculated. Constraints against MCM's on similar to 1-4 h(-1)Gpc scales have been claimed, but relate more to inconsistent assumptions on p erturbation statistics rather than just to topology. Candidate 3-manifolds based on hypothesised multiply imaged objects are being offered for observa tional refutation. The theoretical and observational sides of this rapidly developing subject have yet to make any serious contact, but the prospects of a significant de tection in the coming decade may well propel the two together.