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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: June 24, 2003
MathSciNet review: 1990576
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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: http://dx.doi.org/10.1090/S0002-9947-03-03249-5
PII: S 0002-9947(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