Adiabatic decomposition of the zeta-determinant of the Dirac Laplacian I. The case of an invertible tangential operator. With an appendix by Yoonweon Lee

TL;DR

This paper investigates how to decompose the zeta-determinant of the Dirac Laplacian into contributions from manifold parts, focusing on cases with an invertible tangential operator, advancing spectral geometry understanding.

Contribution

It introduces a method for decomposing the zeta-determinant of the Dirac Laplacian in the presence of an invertible tangential operator, extending previous spectral analysis techniques.

Findings

Decomposition formula for zeta-determinant established

Application to manifolds with invertible tangential operators demonstrated

Enhanced understanding of spectral contributions from manifold parts

Abstract

we discuss the decomposition of the zeta-determinant of the square of the Dirac operator into the contributions coming from the different parts of the manifold in the case of an invertible tangential operator.