Scattering matrices and analytic torsions

2016/05/31 by Martin Puchol, Yeping Zhang, Jialin Zhu
Mathematics · #Adiabatic process #Advanced Operator Algebra Research #Asymptotic expansion #Cylinder #Geometry and complex manifolds #Limit (mathematics) #Scattering #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #math.DG

paper · pdf · doi:10.2140/apde.2021.14.77

published as Analysis & PDE 14 (2021) 77-134 · 56 pages

openalex created_date 2016/06/24 · arxiv created 2019/03/05 · openalex publication_date 2021/02/19 · arxiv updated 2021/02/24 · openalex updated_date 2026/08/05

Abstract

For a compact manifold, which has a part isometric to a cylinder of finite length, we consider an adiabatic limit procedure, in which the length of the cylinder tends to infinity. We study the asymptotic of the spectrum of Hodge-Laplacian and the asymptotic of the L²-metric on de Rham cohomology. As an application, we give a pure analytic proof of the gluing formula for analytic torsion.

Citations

• Massless higher spins and holography
• Analytic torsion and holomorphic determinant bundles I. Bott-Chern forms and analytic torsion
• R-Torsion and the Laplacian on Riemannian manifolds
• Homotopieringe und Linsenräume