The gluing formula of the refined analytic torsion for an acyclic Hermitian connection

Abstract

In the previous work ([14]) we introduced the well-posed boundary conditions ${\mathcal{P}}_{-,{\mathcal{L}}_0}$ and ${\mathcal{P}}_{+,{\mathcal{L}}_1}$ for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the gluing formula of the refined analytic torsion for an acyclic Hermitian connection with respect to the boundary conditions ${\mathcal{P}}_{-,{\mathcal{L}}_0}$ and ${\mathcal{P}}_{+,{\mathcal{L}}_1}$. In this case the refined analytic torsion consists of the Ray-Singer analytic torsion, the eta invariant and the values of the zeta functions at zero. We first compare the Ray-Singer analytic torsion and eta invariant subject to the boundary condition ${\mathcal{P}}_{-,{\mathcal{L}}_0}$ or ${\mathcal{P}}_{+,{\mathcal{L}}_1}$ with the Ray-Singer analytic torsion subject to the relative (or absolute) boundary condition and eta invariant subject to the APS boundary condition on a compact manifold with boundary. Using these results together with the well known gluing formula of the Ray-Singer analytic torsion subject to the relative and absolute boundary conditions and eta invariant subject to the APS boundary condition, we obtain the main result.

References in corpus (1)

• Gluing Formula for Refined Analytic Torsion

Cited by in corpus (1)

• The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary