What is called analytic torsion or Ray-Singer torsion (Ray-Singer 73) is the invariant of a Riemannian manifold given by a product of powers of the functional determinants of the Laplace operators on the manifold acting on the space of differential p-forms:
This analytic torsion is an analogue in analysis of the invariant of topological manifolds called Reidemeister torsion. The two agree for the compact Riemannian manifolds (Cheeger 77).
D. Ray, Isadore Singer, Analytic torsion for complex manifolds, Ann. Math. 98, 1 (1973), 154–177.
Jeff Cheeger, Analytic torsion and Reidemeister torsion, Proc. Natl. Acad. Sci. USA 74, No. 7, pp. 2651-2654 (1977), pdf
Wikipedia, Analytic torsion
A.A. Bytsenko, A.E. Goncalves, W. da Cruz, Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory (arXiv:hep-th/9805187)
Revised on September 2, 2014 19:34:25
by Urs Schreiber