Asymptotic expansions of the zeta-determinants of Dirac Laplacians on a compact manifold with boundary (Q2508670)

The author discusses the asymptotic expansions of the zeta-determinants of Dirac Laplacians with the Dirichlet or the Atiyah-Patodi-Singer (APS) boundary condition on a compact manifold with boundary when the boundary part is stretched. Using the main results, the author obtains the formula describing the ratio of two zeta-determinants of Dirac Laplacians with the APS boundary conditions associated with two unitary involutions. Finally, the author proves the adiabatic decomposition formulas for the zeta-determinants of Dirac Laplacians on a closed manifold when the Dirichlet or the APS boundary condition is imposed on partitioned manifolds.