The Analytic Torsion of the cone over an odd dimensional manifold

We study the analytic torsion of the 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 also prove that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem for a manifold with boundary, according to Bruning and Ma, either in the case that W is an odd sphere or has dimension smaller than six. It follows in particular that the Cheeger Muller theorem holds for the cone over an odd dimensional sphere. We also prove Poincare duality for the analytic torsion of a cone.