On the gluing problem for the spectral invariants of Dirac operators

In this paper, we solve the gluing problem for the ζ-determinant of a Dirac Laplacian. To do so, we develop a new approach to solve such problems which relies heavily on the theory of elliptic boundary problems, the analysis of the resolvent of the Dirac operator, and the introduction of an auxiliary model problem. Moreover, as a byproduct of our approach we obtain a new gluing formula for the eta invariant au gratis.