Vol. 14, No. 1, 2021

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Scattering matrices and analytic torsions

Martin Puchol, Yeping Zhang and Jialin Zhu

Vol. 14 (2021), No. 1, 77–134
Abstract

We consider a compact manifold with a piece isometric to a (finite-length) cylinder. By making the length of the cylinder tend to infinity, we obtain an asymptotic gluing formula for the zeta determinant of the Hodge Laplacian and an asymptotic expansion of the torsion of the corresponding long exact sequence of cohomology equipped with ${L}^{2}$-metrics. As an application, we give a purely analytic proof of the gluing formula for analytic torsion.

Keywords
analytic torsion, scattering theory
Primary: 58J52
Milestones
Received: 28 June 2018
Revised: 28 August 2019
Accepted: 25 October 2019
Published: 19 February 2021
Authors
 Martin Puchol Université Paris-Saclay, CNRS Laboratoire de Mathématiques d’Orsay Orsay France Yeping Zhang School of Mathematics Korea Institute for Advanced Study Seoul South Korea Jialin Zhu Mathematical Science Research Center Chongqing University of Technology Chongqing China