The BFK type gluing formula for zeta-determinants of Dirac Laplacians with the APS boundary conditions

초록

In this note we explain the concept of zeta-determinants of elliptic differential operators and the BFK-gluing formula for zeta-determinants given by Burghelea, Friedlander and Kappeler. We next introduce compatible Dirac operators and their well-posed boundary conditions including the APS boundary conditions and the Calderon projectors. Then we give some results of the gluing formula for zeta-determinants of Dirac Laplacians with respect to the APS boundary conditions. We finally discuss some results of the relative zeta-determinants of Dirac Laplacians on a compact manifold with cylindrical end.