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

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 L2-metrics. As an application, we give a purely analytic proof of the gluing formula for analytic torsion.

analytic torsion, scattering theory
Mathematical Subject Classification 2010
Primary: 58J52
Received: 28 June 2018
Revised: 28 August 2019
Accepted: 25 October 2019
Published: 19 February 2021
Martin Puchol
Université Paris-Saclay, CNRS
Laboratoire de Mathématiques d’Orsay
Yeping Zhang
School of Mathematics
Korea Institute for Advanced Study
South Korea
Jialin Zhu
Mathematical Science Research Center
Chongqing University of Technology