Abelian analytic torsion and symplectic volume

B.D.K. McLellan

Address: Northeastern University, Department of Mathematics, 360 Huntington Ave, Boston, MA, USA, 02115

E-mail: b.mclellan@neu.edu

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.

AMSclassification: primary 58J28; secondary 53D10, 53C25.

Keywords: analytic torsion, contact torsion, Chern-Simons theory, Sasakian three-manifold, quantum field theory.

DOI: 10.5817/AM2015-3-175