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 $\varphi$-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 $\varphi$- and incomplete wedge-metrics. As a simple consequence we recover a result by Sher and Guillarmou about analytic torsion under conic degeneration.

38 pages,10 figures

References in corpus (4)

• Index Theory for Coverings
• Scattering configuration spaces
• Low energy limit for the resolvent of some fibered boundary operators
• Analytic torsion on manifolds with fibred boundary metrics