The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions

Abstract

The odd signature operator is a Dirac operator which acts on the space of differential forms of all degrees and whose square is the usual Laplacian. We extend the result of [15] to prove the gluing formula of the zeta-determinants of Laplacians acting on differential forms of all degrees with respect to the boundary conditions ${\mathcal{P}}_{-,{\mathcal{L}}_0}$, ${\mathcal{P}}_{+,{\mathcal{L}}_1}$. We next consider a double of de Rham complexes consisting of differential forms of all degrees with the absolute and relative boundary conditions. Using a similar method, we prove the gluing formula of the zeta-determinants of Laplacians acting on differential forms of all degrees with respect to the absolute and relative boundary conditions.

19 pages

References in corpus (4)

• Zero Sets of Solutions to Semilinear Elliptic Systems of First Order
• Gluing Formula for Refined Analytic Torsion
• The refined analytic torsion and a well-posed boundary condition for the odd signature operator
• The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary