Bob Gardner's "Topology, Cosmology and Shape of Space" Talk, Section 4

TOPOLOGY, COSMOLOGY AND THE SHAPE OF SPACE

4. Hyperbolic Universes

A saddle shaped surface has negative curvature and hyperbolic geometry (in which the sum of the angles of a triangle is less than 180 degrees).

Some think the universe has this shape, only raised up a dimension. In fact, much empirical evidence suggests that the universe has negative curvature. In this case, the universe will expand forever. This is another example of an open universe. In this particular model, the universe is infinite, but there exist hyperbolic models of the universe which are finite.

Goto Section 5.