Burghelea-Friedlander-Kappeler's gluing formula and the adiabatic decomposition of the zeta-determinant of a Dirac Laplacian (Q1401491)

The author presents a relation between the zeta-determinant of a Dirac Laplacian with Dirichlet boundary conditions and Atiyah-Patodi-Singer boundary conditions on a compact oriented Riemannian manifold having a product structure near a hypersurface. This leads to an adiabatic decomposition theorem for the zeta-determinant of a Dirac Laplacian extending an analogous statement by \textit{J. Park} and \textit{K. P. Wojciechowski} [Commun. Partial Differ. Equations 27, 7--8, 1407--1465 (2002; Zbl 1016.58020)] to even-dimensional manifolds.