  In this note we specialize and illustrate the ideas developed in the paper
math.DG/0201112 of the first author ("Index theory, eta forms, and Deligne
cohomology ") in the case of the determinant line bundle. We discuss the
surgery formula in the adiabatic limit using the adiabatic decomposition
formula of the zeta regularized determinant of the Dirac Laplacian obtained by
the second author and K. Wojciechowski.
