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2021 Scattering matrices and analytic torsions
Martin Puchol, Yeping Zhang, Jialin Zhu
Anal. PDE 14(1): 77-134 (2021). 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.

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Martin Puchol. Yeping Zhang. Jialin Zhu. "Scattering matrices and analytic torsions." Anal. PDE 14 (1) 77 - 134, 2021. https://doi.org/10.2140/apde.2021.14.77

Information

Received: 28 June 2018; Revised: 28 August 2019; Accepted: 25 October 2019; Published: 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2140/apde.2021.14.77

Subjects:
Primary: 58J52

Keywords: analytic torsion , scattering theory

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 1 • 2021
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