Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

Author:
Yoonweon Lee

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4093-4110

MSC (2000):
Primary 58J52, 58J50

DOI:
https://doi.org/10.1090/S0002-9947-03-03249-5

Published electronically:
June 24, 2003

MathSciNet review:
1990576

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Abstract | References | Similar Articles | Additional Information

Abstract: The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under an assumption that the product structure is given near the boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dirichlet and Neumann boundary conditions and of the analytic torsion with respect to the absolute and relative boundary conditions.

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Additional Information

**Yoonweon Lee**

Affiliation:
Department of Mathematics, Inha University, Inchon, 402-751, Korea

Email:
ywlee@math.inha.ac.kr

DOI:
https://doi.org/10.1090/S0002-9947-03-03249-5

Keywords:
Zeta-determinant,
gluing formula,
Laplacian,
Dirichlet (Neumann) boundary condition,
absolute (relative) boundary condition,
adiabatic decomposition

Received by editor(s):
April 15, 2002

Received by editor(s) in revised form:
October 10, 2002

Published electronically:
June 24, 2003

Additional Notes:
The author was partially supported by Korea Research Foundation Grant KRF-2000-015-DP0045

Article copyright:
© Copyright 2003
American Mathematical Society