The zeta-determinants and BFK-gluing formula

초록

Zeta-determinant is a global spectral invariant, which plays an important role in the theory of the analytic torsion. In this talk, we review the definition of the zeta-determinant and analytic torsion, and give some computations and geometric applications of the zeta-determinants. We next discuss the BFK-gluing formula of the zeta-determinant of Laplacians given by Burghelea, Friedlander and Kappeler and give some applications of BFK-gluing formula to the relative zeta-determinants on a manifold with cylindrical ends or cusps and the gluing formula of the Dolbeault Laplacian on a compact Riemann surface discussed by Wentworth.