Complex-valued Ray-Singer torsion

DOI10.1016/j.jfa.2007.03.027zbMath1131.58020arXivmath/0604484OpenAlexW2035037633MaRDI QIDQ2373796

Dan Burghelea, Stefan Haller

Publication date: 16 July 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0604484

zbMATH Keywords

Euler structuresdeterminant lineRay-Singer torsionFranz-Reidemeister torsionMilnor-Turaev torsion

Mathematics Subject Classification ID

Determinants and determinant bundles, analytic torsion (58J52) Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. (57Q10)

Related Items (18)

Euler structures, the variety of representations and the Milnor-Turaev torsion ⋮ Analytic torsion of generic rank two distributions in dimension five ⋮ Refined analytic torsion as analytic function on the representation variety and applications ⋮ Ray-Singer type theorem for the refined analytic torsion ⋮ Complex valued Bismut-Lott index theorem ⋮ Anomaly formulas for the complex-valued analytic torsion on compact bordisms ⋮ The refined analytic torsion and a well-posed boundary condition for the odd signature operator ⋮ Co-Euler structures on bordisms ⋮ A Cheeger-Müller theorem for symmetric bilinear torsions ⋮ Comparison of the refined analytic and the Burghelea-Haller torsions ⋮ Burghelea-Haller analytic torsion of $\mathbb {Z}_{2}$-graded elliptic complexes ⋮ A Cheeger-Müller theorem for symmetric bilinear torsions on manifolds with boundary ⋮ Cappell-Miller analytic torsion for manifolds with boundary ⋮ Complex valued Ray-Singer torsion II ⋮ A Cheeger-Müller theorem for Cappell-Miller torsions on manifolds with boundary ⋮ Refined analytic torsion on manifolds with boundary ⋮ Burghelea-Haller analytic torsion for manifolds with boundary ⋮ Complex‐valued analytic torsion for flat bundles and for holomorphic bundles with (1,1) connections

Cites Work

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• Morse homology
• On the determinant of elliptic differential and difference finite operators in vector bundles over \(S^ 1\)
• Euler structures, the variety of representations and the Milnor-Turaev torsion
• Ray-Singer type theorem for the refined analytic torsion
• Refined analytic torsion as an element of the determinant line
• A Cheeger-Müller theorem for symmetric bilinear torsions
• Superconnections, Thom classes, and equivariant differential forms
• A short proof of the local Atiyah-Singer index theorem
• Analytic torsion and R-torsion of Riemannian manifolds
• Analytic torsion and the heat equation
• Removing metric anomalies from Ray-Singer torsion
• Characteristic forms and geometric invariants
• Asymptotic expansion of the Witten deformation of the analytic torsion
• Comparison of the refined analytic and the Burghelea-Haller torsions
• Refined analytic torsion
• R-torsion and the Laplacian on Riemannian manifolds
• A refinement of the Ray-Singer torsion
• EULER STRUCTURES, NONSINGULAR VECTOR FIELDS, AND TORSIONS OF REIDEMEISTER TYPE
• Complex valued Ray-Singer torsion II
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Analytic torsion and Reidemeister torsion
• Poincar\'e--Reidemeister metric, Euler structures, and torsion
• Dynamics, Laplace transform and spectral geometry
• Whitehead torsion
• Riemannian geometry and geometric analysis

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