The invariant integration method for Chern-Simons theory defined on compact
hyperbolic spaces of the form Gamma\H-3 is verified in the semiclassical a
pproximation. The semiclassical limit for the partition function is calcula
ted. The contribution to the sum over topologies in three-dimensional quant
um gravity is briefly discussed. (C) 1999 American Institute of Physics. [S
0021-3640(99)00114-0].