  A topologically finite universe, smaller than the observable horizon, will
have circles-in-the-sky: pairs of circles around which the temperature
fluctuations in the cosmic microwave background are correlated. The circles
occur along the intersection of copies of the spherical surface of last
scattering. For any observer moving with respect to the microwave background,
the circles will be deformed into ovals. The ovals will also be displaced
relative to the direction they appear in a comoving frame. The displacement is
the larger of the two effects. In a Lorenz boosted frame, the angular
displacement of a point on the surface of last scattering relative to the
comoving frame is proportional to the velocity. For the Earth's motion, the
effect is on the order of 0.14 degrees at the very worst. If we live in a small
universe and are looking for an identical copy of a spot in the sky, it may be
displaced by as much as 0.14 degrees from where we expect. This can affect all
pattern based searches for the topology of the universe. In particular,
high-resolution searches for circle pairs could be off by this much.
