A Cheeger-Müller theorem for symmetric bilinear torsions on manifolds with boundary

Abstract

In this paper, we extend Su-Zhang’s Cheeger-Muller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Bruning-Ma’s Cheeger-Muller type theorem for Ray-Singer metric on manifolds with boundary to symmetric bilinear torsions in product case. We also compare it with the Ray-Singer analytic torsion on manifolds with boundary.