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.

arXiv comment38 pages,10 figures

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