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

transactions of the american mathematical society

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