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Scattering matrices
and analytic torsions
Martin Puchol, Yeping Zhang and Jialin Zhu |
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Vol. 14 (2021), No. 1, 77–134
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Abstract |
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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 -metrics. As an application, we give a purely analytic proof of the gluing formula for analytic torsion. |
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Keywords
analytic torsion, scattering theory
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Mathematical Subject Classification 2010
Primary: 58J52
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Milestones
Received: 28 June 2018
Revised: 28 August 2019
Accepted: 25 October 2019
Published: 19 February 2021
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Authors |
| Martin Puchol | |
| Université Paris-Saclay, CNRS Laboratoire de Mathématiques d’Orsay Orsay France |
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| Yeping Zhang | |
| School of Mathematics Korea Institute for Advanced Study Seoul South Korea |
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| Jialin Zhu | |
| Mathematical Science Research
Center Chongqing University of Technology Chongqing China |
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