Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory

TL;DR

This paper verifies the invariant integration method for SU(2) Chern-Simons theory on hyperbolic 3-manifolds in the semiclassical limit, analyzing torsions and presenting results for connected sums of such manifolds.

Contribution

It provides a verification of the invariant integration method in the semiclassical approximation for hyperbolic 3-manifolds and discusses torsions in manifolds with boundary.

Findings

Verification of the invariant integration method in the semiclassical limit.

Presentation of the semiclassical limit for connected sums of hyperbolic 3-manifolds.

Discussion of L^2-analytical and topological torsions of manifolds with boundary.

Abstract

The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of hyperbolic 3-manifolds is presented. We discuss briefly L^2 - analytical and topological torsions of a manifold with boundary.