The invariant integration method for Chern-Simons theory defined on the com
pact hyperbolic manifold Gamma\H-3 is verified in the semiclassical approxi
mation. The semiclassical limit for the partition function is presented. We
discuss briefly L-2-analytic torsion and the eta invariant of Atiyah-Patod
i-Singer for compact hyperbolic 3-manifolds. (C) 1999 Published by Elsevier
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