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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Mayer-Vietoris formula for the determinant of a Laplace operator on an even-dimensional manifold


Author: Yoonweon Lee
Journal: Proc. Amer. Math. Soc. 123 (1995), 1933-1940
MSC: Primary 58G26
DOI: https://doi.org/10.1090/S0002-9939-1995-1254845-7
MathSciNet review: 1254845
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Abstract: Let $\Delta$ be a Laplace operator acting on differential p-forms on an even-dimensional manifold M. Let $\Gamma$ be a submanifold of codimension 1. We show that if B is a Dirichlet boundary condition and R is a Dirichlet-Neumann operator on $\Gamma$, then ${\operatorname {Det}}(\Delta + \lambda ) = {\operatorname {Det}}(\Delta + \lambda ,B){\operatorname {Det}}(R + \lambda )$ and ${\operatorname {Det}^ \ast }\Delta = \frac {1}{{{{(\det A)}^2}}}{\operatorname {Det}}(\Delta ,B){\operatorname {Det}^ \ast }R$. This result was established in 1992 by Burghelea, Friedlander, and Rappeler for a 2-dimensional manifold with $p = 0$.


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Article copyright: © Copyright 1995 American Mathematical Society