Complex-valued Ray–Singer torsion

2006/04/30 by Dan Burghelea, Stefan Haller · 1 citation
Computer Science · Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Conjecture #Geometric Analysis and Curvature Flows #Invariant (physics) #Mathematical physics #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #Torsion (gastropod) #math.DG #msc:57R20 #msc:58J52

paper · pdf · doi:10.1016/j.jfa.2007.03.027

published as J. Funct. Anal. 248(2007), 27--78 · Fixed two sign mistakes and added a few more details here and there

arxiv created 2007/02/13 · openalex publication_date 2007/05/11 · arxiv updated 2015/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

In the spirit of Ray and Singer we define a complex valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex valued Reidemeister torsion, including its phase. We establish this conjecture in some non-trivial situations.

Citations

• Heat Kernels and Dirac Operators
• R-Torsion and the Laplacian on Riemannian manifolds
• Characteristic Forms and Geometric Invariants
• A short proof of the local Atiyah-Singer index theorem
• Refined Analytic Torsion

Cited by

• Renormalization of determinant lines in Quantum Field Theory