Scattering matrices and analytic torsions

Abstract

We consider a compact manifold with a piece isometric to a (finite-length) cylinder. By making the length of the cylinder tend to infinity, we obtain an asymptotic gluing formula for the zeta determinant of the Hodge Laplacian and an asymptotic expansion of the torsion of the corresponding long exact sequence of cohomology equipped with $L^2$-metrics. As an application, we give a purely analytic proof of the gluing formula for analytic torsion.