Analytic Torsion for Fibred Boundary Metrics and Conic Degeneration

Abstract We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $\phi $-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete $\phi $- and incomplete wedge-metrics. As a simple consequence we recover a result by Guillarmou and Sher about analytic torsion under conic degeneration.