Milnor and Ray-Singer metrics on the equivariant determinant of a flat vector bundle

DOI10.1007/BF01895837zbMath0830.58030OpenAlexW2027167518MaRDI QIDQ1321626

Jean-Michel Bismut, Weiping Zhang

Publication date: 15 January 1996

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/58160

zbMATH Keywords

analytic torsionMilnor metriccombinatorial torsionWitten complexRay-Singer metric

Mathematics Subject Classification ID

Determinants and determinant bundles, analytic torsion (58J52)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic and topological torsion for manifolds with boundary and symmetry
• The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
• Superconnections, Thom classes, and equivariant differential forms
• Determinants of Cauchy-Riemann operators on a Riemann surface
• A short proof of the local Atiyah-Singer index theorem
• Analytic torsion and holomorphic determinant bundles. I: Bott-Chern forms and analytic torsion. II: Direct images and Bott-Chern forms. III: Quillen metrics on holomorphic determinants
• Analytic torsion for group actions
• Complex immersions and Quillen metrics
• Analytic torsion and R-torsion of Riemannian manifolds
• Analytic torsion and the heat equation
• Homotopieringe und Linsenräume
• On gradient dynamical systems
• Curvature and the eigenvalues of the Laplacian
• Reidemeister torsion and the Laplacian on lens spaces
• Equivariant differential topology
• R-torsion and the Laplacian on Riemannian manifolds
• Complexes à automorphismes et homéomorphic différentiable
• Multiple wells in the semi-classical limit I
• Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells
• Puits multiples en mecanique semi-classique iv etude du complexe de witten
• The projectivity of the moduli space of stable curves. I: Preliminaries on "det" and "Div".
• Whitehead torsion
• Differentiable dynamical systems
• Über die Torsion einer Überdeckung.

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