Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

2003/04/18 by Yoonweon Lee, Lee, Yoonweon
Chemistry · Mathematics · Physics and Astronomy · #58J50 #58J52 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Mechanics and Applications #math.DG #msc:58J50 #msc:58J52

paper · pdf · doi:10.48550/arxiv.math/0304250

24 pages, AMS-Tex

openalex publication_date 2003/04/18 · arxiv created 2003/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under the assumption of the product structure near boundary. As applications of this result,we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.

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