The analytic torsion of a cone over an odd dimensional manifold

Abstract

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W . We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Müller theorem [3,2] for a manifold with boundary, according to Brüning and Ma (2006) [5]. We also prove Poincaré duality for the analytic torsion of a cone.