  The (large angle) COBE DMR data can be used to probe the global topology of
our universe on scales comparable to and just beyond the present ``horizon''.
For compact topologies, the two main effects on the CMB are: [1] the breaking
of statistical isotropy in characteristic patterns determined by the photon
geodesic structure of the manifold and [2] an infrared cutoff in the power
spectrum of perturbations imposed by the finite spatial extent. To make a
detailed confrontation of these effects with the COBE maps requires the
computation of the pixel-pixel temperature correlation function for each
topology and for each orientation of it relative to the sky. We present a
general technique using the method of images for doing this in compact
hyperbolic (CH) topologies which does not require spatial eigenmode
decomposition. We demonstrate that strong constraints on compactness follow
from [2] and that these limits can be improved by exploiting the details of the
geodesic structure for each individual topology ([1]), as we show for the flat
3-torus and selected CH models.
