Heat trace asymptotics, curvature tensors and BFK-gluing formula for zeta-determinants

초록

The gluing formula for the zeta-determinants of Laplacians on a compact Riemannian manifold was proved by Burghelea, Friedlander and Kappeler in 1990’s by using the Dirichlet-to-Neumann operator. In the proof of this formula there appears a real polynomial of degree at least the half of the dimension of the underlying manifold. This polynomial plays an important role in the BFK-gluing formula. Recently we recognized that the coefficients of this polynomial and the heat trace asymptotics of the Dirichlet-to-Neumann operator can be expressed by some curvature tensors such that scalar curvatures and principal curvatures. In this talk we discuss this fact when the cutting hypersurface is a 2-dimensional manifold. This talk is based on the joint work with Klaus Kirsten.