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
نویسنده
چکیده
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 the assumption of the product structure near 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. §
منابع مشابه
Burghelea-friedlander-kappeler’s Gluing Formula and the Adiabatic Decomposition of the Zeta-determinant of a Dirac Laplacian
In this paper we first establish the relation between the zeta-determinant of a Dirac Laplacian with the Dirichlet boundary condition and the APS boundary condition on a cylinder. Using this result and the gluing formula of the zetadeterminant given by Burghelea, Friedlander and Kappeler with some assumptions, we prove the adiabatic decomposition theorem of the zeta-determinant of a Dirac Lapla...
متن کاملThe Ratio of Two Zeta-determinants of Dirac Laplacians Associated with Unitary Involutions on a Compact Manifold with Cylindrical End
Abstract. Given two unitary involutions σ1 and σ2 satisfying Gσi = −σiG on kerB on a compact manifold with cylindrical end, M. Lesch, K. Wojciechowski ([LW]) and W. Müller ([M]) established the formula describing the difference of two eta-invariants with the APS boundary conditions associated with σ1 and σ2. In this paper we establish the analogous formula for the zeta-determinants of Dirac Lap...
متن کاملNew Proof of the Cheeger-müller Theorem
We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinants of elliptic operators. Instead, we provide a direct way of analyzing the behaviour of the determinant of the Witten deformation of th...
متن کاملTorsions for Manifolds with Boundary and Glueing Formulas
We extend the definition of analytic and Reidemeister torsion from closed compact Riemannian manifolds to compact Riemannian manifolds with boundary (M,∂M), given a flat bundle F of A-Hilbert modules of finite type and a decomposition of the boundary ∂M = ∂−M ∪ ∂+M into disjoint components. If the system (M,∂−M,∂+M,F) is of determinant class we compute the quotient of the analytic and the Reide...
متن کاملComplex valued Ray–Singer torsion II
In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003