Compact 3-MANIFOLDS of Negative Curvature

Experimental evidence strongly suggests that Ω_matter ≃ 0.3. Until recently, many cosmologists favored a vanishing cosmological constant Λ = 0, and there was considerable interest in models of a hyperbolic (that is, negatively curved) universe. In particular, cosmologists investigating compact, multiply connected models worked in the realm of compact hyperbolic 3-manifolds. Interest in these models has recently diminished because studies of distant supernovae [1,2] and the microwave background [3,4] suggest Ω_Λ ≃ 0.7 and Ω_total ≃ 1.0, implying a flat universe. On the other hand, particle physicists investigating higher-dimensional models of spacetime now have an interest in compact hyperbolic manifolds, so the basic mathematics is relevant in a new context...