Determinant bundles, boundaries, and surgery

Abstract

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 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 in [Scattering theory, the adiabatic decomposition of the zeta-determinant and the Dirichlet to Neumann operator, Preprint]. (C) 2004 Published by Elsevier B.V.