Scattering matrices and analytic torsions

Puchol, Martin; Zhang, Yeping; Zhu, Jialin

doi:10.2140/apde.2021.14.77

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Scattering matrices and analytic torsions

Martin Puchol, Yeping Zhang and Jialin Zhu

Vol. 14 (2021), No. 1, 77–134

DOI: 10.2140/apde.2021.14.77

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

Mathematical Subject Classification 2010

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

Vol. 14, No. 1, 2021