Abelian Analytic Torsion and Symplectic Volume

TL;DR

This paper links abelian analytic torsion on Sasakian three-manifolds to symplectic volume, providing explicit calculations using Seifert data, thus advancing understanding of geometric invariants in this setting.

Contribution

It explicitly identifies abelian analytic torsion as a multiple of the symplectic volume form on the moduli space, with calculations based on Seifert data.

Findings

Analytic torsion is proportional to the symplectic volume form.

Explicit formulas for torsion in terms of Seifert data.

Connection between torsion and geometric structures on Sasakian manifolds.

Abstract

This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.