CAN COBE SEE THE SHAPE OF THE UNIVERSE

In recent years, the large angle COBE-DMR data have been used to place constraints on the size and shape of certain. topologically compact m odels of the universe. Here we show that this approach does not work f or generic compact models. In particular, we show that compact hyperbo lic models do not suffer the same loss of large angle power seen in fl at or spherical models. This follows from applying a topological theor em to show that generic hyperbolic three manifolds support long wavele ngth fluctuations, and by taking into account the dominant role played by the integrated Sachs-Wolfe effect in a hyperbolic universe.