Ray-Singer Torsion for a Hyperbolic 3-Manifold and Asymptotics of Chern-Simons-Witten Invariant

Abstract

The Ray-Singer torsion for a compact smooth hyperbolic 3-dimensional manifold ${\mathcal{H}}^3$ is expressed in terms of Selberg zeta-functions, making use of the associated Selberg trace formulae. Applications to the evaluation of the semiclassical asymptotics of the Witten's invariant for the Chern-Simons theory with gauge group SU(2) as well as to the sum over topologies in 3-dimensional quantum gravity are presented.

Latex file, 15 pages. Some improvements, grammatical mistakes and typos corrected

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