On the Orthogonal Decomposition of a Flat Symmetric Bilinear Form

In this paper, we proved a theorem on the orthogonal decomposition of a flatsymmetric bilinear form. If the nullity space of a flat symmetric bilinear formis not too large, it can be decomposed into two bilinear forms, one of which isnull, the other is flat and has a large nullity.

A Cheeger-Mller Theorem for Symmetric Bilinear Torsions

The authors establish a Cheeger-Müller type theorem for the complex valued analytic torsion introduced by Burghelea and Hailer for fiat vector bundles carrying nondegenerate symmetric bilinear forms. As a consequence, they prove the Burghelea-Haller conjecture in full generality, which gives an analytic interpretation of （the square of） the Turaev torsion.

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

In this paper,we extend Su-Zhang’s Cheeger-Mller 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 Brning-Ma’s Cheeger-Mller 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.

Zero Product Determined Jordan Algebras, II

The Albert algebra and the Jordan algebra of a nondegenerate symmetric bilinear form are shown to be zero product determined.