Refined Analytic Torsion: Comparison Theorems and Examples
Rung-Tzung Huang

Abstract: Recently, Braverman and Kappeler introduced "refined analytic torsion" associated to a complex flat vector bundle over a closed odd dimensional manifold and computed the ratio between refined analytic torsion and the Turaev torsion. On a different line of thoughts, Burghelea and Haller introduced "complex Ray-Singer torsion" associated to a nondegenerate symmetric bilinear form on a complex flat vector bundle over an arbitrary dimensional closed manifold and made a conjecture about the relationship between complex Ray-Singer torsion and the Turaev torsion. In this talk I will present different results establishing the relationships among refined analytic torsion, complex Ray-Singer torsion and Turaev torsion. I will also present the formula of refined analytic torsion of lens spaces.