Gluing formula of the refined analytic torsion

초록

The refined analytic torsion was introduced by Braverman and Kappeler on an odd dimensional closed Riemannian manifold in 2000's as an analytic analogue of the Turav torsion. It is defined by using the spectrum of the odd signature operator and is described as an element of the determinant line for cohomologies. Specially, when the odd signature operator is defined by an acyclic Hermitian connection, the refined analytic torsion is a complex number whose modulus part is a classical Ray-Singer analytic torsion and the phase part is the rho invariant, the difference of two eta invariants. In earlier work we introduced a well-posed boundary condition for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this talk we discuss the gluing formula for the refined analytic torsion on a closed Riemannian manifold with respect to this boundary condition in case that the odd signature operator is defined by an acyclic Hermitian connection. Basic tools are BFK-gluing formula for the zeta-determinants and the gluing formula of eta invariant given by Breuning, Lesch and Kirk.