Abelian Analytic Torsion and Symplectic Volume
Brendan McLellan

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology
