BFK-type gluing formula for zeta-determinants of Dirac Laplacians

초록

The zeta-determinant of a Dirac Laplacian on a compact manifold is a global spectral invariant, which plays a central role in the theory of the analytic torsion. The gluing formula for the zeta-determinants of Laplacians was proven by Burghelea, Friedlander and Kappeler with respect to the Dirichlet boundary condition. A Dirac Laplacian is a square of a Dirac operator, which is a first order elliptic operator. In this talk we discuss the gluing formula of the zeta-determinants of Dirac Laplacians with respect to well-posed boundary conditions to Dirac type operators in the sense of Seeley including the Atiyah-Patodi-Singer boundary condition.