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
MathSciNet review: 1254845
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G26

Retrieve articles in all journals with MSC: 58G26

Additional Information

Article copyright: © Copyright 1995 American Mathematical Society