Journal of Geometry and Physics 52 (2004) 28–43 Determinant bundles, boundaries, and surgery

In this note we specialize and illustrate the ideas developed in the paper [Index theory, eta forms, and Deligne cohomology] Families, Eta forms, and Deligne cohomology in the case of the determi-nant line bundle. We discuss the surgery formula in the adiabatic limit using the adiabatic decom-position formula of the zeta regularized determinant of the Dirac Laplacian in [Scattering theory, the adiabatic decomposition of the ζ-determinant and the Dirichlet to Neumann operator, Preprint]