Boundary problem for the refined analytic torsion on compact manifolds with boundary

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 Turaev torsion. It is defined by using the graded zeta-determinant of the odd signature operator and is described as an element of the determinant line for cohomologies. In this note we briefly discuss the boundary problem for the refined analytic torsion on a compact Riemannian manifold with boundary by introducing well posed boundary conditions for the odd signature operator. We also discuss the gluing formula for the refined analytic torsion on a closed Riemannian manifold with respect to our chosen boundary conditions