The Topology of the Universe
  The Hilbert-Einstein equations are insufficient to describe the geometry of the Universe, as they only constrain a local geometrical property: curvature. A global knowledge of the geometry of space, if possible, would require measurement of the topology of the Universe. Since the subject was discussed in 1900 by Schwarzschild, observational attempts to measure global topology have been rare for most of this century, but have accelerated in the 1990's due to the rapidly increasing amount of observations of non-negligible fractions of the observational sphere. A brief review of basic concepts of cosmic topology and of the rapidly growing gamut of diverse and complementary observational strategies for measuring the topology of the Universe is provided here. 
Boudewijn F. Roukema (IUCAA)