Speaker : Prof. Yoonweon Lee (Inha University, Korea)
Title : A polynomial associated to the BFK-gluing formula for zeta-determinants and some curvature tensors
Time : 2017-08-18 (Fri) 10:30 - 11:30
Place : Seminar Room 617, Institute of Mathematics (NTU Campus)
Abstract: The gluing formula for zeta-determinants of Laplacians is proved by Burghelea, Friedlander and Kappeler (BFK) in 1990’s by using the Dirichlet-to-Neumann operator. In the proof of the BFK-gluing formula there appears a polynomial of degree at most the half of an ambient manifold. This polynomial is determined completely by the Laplacians on an arbitrary small collar neighborhood of the cutting hypersurface and the coefficients are important ingredient in the BFK-gluing formula. Recently, we recognize that the coefficients of this polynomial can be expressed by some intrinsic and extrinsic curvature tensors including the scalar curvatures and principal curvatures. In this talk, we will go through the proof of the BFK-gluing formula for Laplacians on a compact Riemannian manifold in a self-contained way. Then, we will discuss this polynomial when a warped product metric is given near the cutting hypersurface. Finally, we will discuss how these coefficients can be expressed by some curvature tensors when the cutting hypersurface is a 2-dimensional compact oriented Riemannian manifold. This talk is based on the joint work with Klaus Kirsten.