ABSTRACT
Exercise 22.2 (a) Trace around the circle centered in the western sky of Figure 22.8 using your left index finger, starting at point A and going counterclockwise, while simultaneously tracing around the circle in the eastern sky with your right index finger, starting at point A' and going clockwise. Do your fingers pass over equal temperatures at corresponding points? (b) Locate the circles centered in the northern and southern skies. Do they also have equal temperatures at corresponding points? □
Exercise 22.3 (a) If the universe of Figure 22.8 were a quarter turn manifold instead of a three-torus, how would that affect the matching circles? (b) If it were K2 X S1, how would that affect the match ing circles? □
Exercise 22.4 How would the matching circles ap pear in the Poincare dodecahedral space? How about in the Seifert-Weber space? By studying the match ing circles alone, could you decide whether you were living in a Poincare universe or a Seifert-Weber uni verse? □
Neil Cornish, David Spergel, and Glenn Starkman were the first people to realize that in a suffi ciently small multiconnected universe the last scat-
tering surface intersects itself, and the circles of intersection reveal the shape of the space.
