Burghelea-Friedlander-Kappeler's gluing formula and the adiabatic decomposition of the zeta-determinant of a Dirac Laplacian
نویسندگان
چکیده
منابع مشابه
Burghelea-friedlander-kappeler’s Gluing Formula and the Adiabatic Decomposition of the Zeta-determinant of a Dirac Laplacian
In this paper we first establish the relation between the zeta-determinant of a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary condition on a cylinder. Using this result and the gluing formula of the zetadeterminant given by Burghelea, Friedlander and Kappeler with some assumptions, we prove the adiabatic decomposition theorem of the zeta-determinant of a Dirac Lapla...
متن کاملBurghelea-friedlander-kappeler’s Gluing Formula for the Zeta-determinant and Its Applications to the Adiabatic Decompositions of the Zeta-determinant and the Analytic Torsion
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 Dir...
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We discuss the decompositon of the ζ-determinant of the square of the Dirac operator into contributions coming from the different parts of the manifold. The “easy” case was worked out in the paper [12]. Due to the assumptions made on the operators in [12], we were able to avoid the presence of the “small eigenvalues”, which provide the large time contribution to the determinant. In the present ...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2003
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-003-0370-8