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

2013/12/04 by Guangxiang Su, Su, Guangxiang
Mathematics · #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.1312.1264

Abstract

In this paper, we extend Su-Zhang's Cheeger-Mueller 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 Bruening-Ma's Cheeger-Mueller 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.

Citations

• On the heat equation and the index theorem

Related

• Generalized Ray-Singer conjecture. I. A manifold with a smooth boundary
• Analytic Torsion and R-Torsion for Manifolds with Boundary
• An L²-Cheeger Müller theorem on compact manifolds-with-boundary
• Survey on analytic and topological torsion
• Cappell-Miller analytic torsion for manifolds with boundary