BurgheleaFriedlanderKappeler's gluing formula for the zetadeterminant and its applications to the adiabatic decompositions of the zetadeterminant and the analytic torsion
Author:
Yoonweon Lee
Journal:
Trans. Amer. Math. Soc. 355 (2003), 40934110
MSC (2000):
Primary 58J52, 58J50
Published electronically:
June 24, 2003
MathSciNet review:
1990576
Fulltext PDF Free Access
Abstract 
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Abstract: The gluing formula of the zetadeterminant 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 zetadeterminant 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, 402751, Korea
Email:
ywlee@math.inha.ac.kr
DOI:
http://dx.doi.org/10.1090/S0002994703032495
PII:
S 00029947(03)032495
Keywords:
Zetadeterminant,
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 KRF2000015DP0045
Article copyright:
© Copyright 2003
American Mathematical Society
