Gluing Formula for Refined Analytic Torsion

Abstract

In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without boundary. We now derive a gluing formula for our construction, which can be viewed as a gluing law for the original definition of refined analytic torsion by Braverman and Kappeler. A gluing formula allows to compute the torsion invariant by cutting the manifold into elementary pieces and performing computations on each component. Certainly, the general fact of existence of such gluing formulas is remarkable from the analytic point of view, since the secondary spectral invariants are uppermost non-local.

Some references were corrected. 45 pages, 1 figure

References in corpus (3)

• Functional Determinants for Regular-Singular Laplace-type Operators
• On boundary value problems for Dirac type operators. I. Regularity and self-adjointness
• Refined Analytic Torsion on Manifolds with Boundary

Cited by in corpus (5)

• The refined analytic torsion and a well-posed boundary condition for the odd signature operator
• The gluing formula of the refined analytic torsion for an acyclic Hermitian connection
• The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary
• Refined Analytic Torsion on Manifolds with Boundary
• The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions