Glenn Starkman
Case Western

Circles in the Sky: 
Determining the Universe's Topology 
with the Microwave Background Radiation

If $\Omega<1$, and the universe is negatively curved,
topology on scales significantly smaller than the horizon 
is expected and not ruled out.
Previous contraints on topology were specific to flat space, $\Omega=1$,
and do not apply to negatively-curved space.
If the universe is topologically interesting
then generically the signature of the
topology of the universe is writ clearly on the cosmic 
microwave background sky.
We expect to find many many pairs of circles
in the sky around which the fluctuations in the CMBR 
are strongly correlated with one another.
Furthermore, if we find such circle pairs, we will be able
to accurately reconstruct the shape of the universe and 
determine our position in it.