The BFK-gluing formula and relative determinants on manifolds with cusps

In this paper we use the BFK-gluing formula for zeta-determinants to express the relative determinant of Laplacians on a manifold with cusps by the product of the determinant of a Laplacian on a compact manifold with boundary augmented by the Dirichlet condition and the determinant of the Dirichlet-...

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Bibliographic Details
Published inJournal of geometry and physics Vol. 117; pp. 197 - 213
Main Authors Kirsten, Klaus, Lee, Yoonweon
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2017
Subjects
BFK-gluing formula
Dirichlet-to-Neumann operator
Manifold with cusps
Relative determinant
secondary
Manifold with cusps
Dirichlet-to-Neumann operator
Relative determinant
BFK-gluing formula
primary
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Summary:In this paper we use the BFK-gluing formula for zeta-determinants to express the relative determinant of Laplacians on a manifold with cusps by the product of the determinant of a Laplacian on a compact manifold with boundary augmented by the Dirichlet condition and the determinant of the Dirichlet-to-Neumann operator and some other ingredients. We use this result to compute some asymptotic expansions of zeta-determinants of Laplacians on a compact manifold with boundary augmented by the Dirichlet condition when we prolong the boundary part to cusps of infinite lengths.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2017.03.013