Equivariant Bott-Chern currents and the Ray-Singer analytic torsion

DOI10.1007/BF01446907zbMath0682.58045OpenAlexW2031590670MaRDI QIDQ1824268

Jean-Michel Bismut

Publication date: 1990

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164699

zbMATH Keywords

heat equationfixed point theorycohomologyparabolic equationindex theoryloop spaceQuillen metrics

Mathematics Subject Classification ID

Index theory and related fixed-point theorems on manifolds (58J20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Duistermaat–Heckman formulas and index theory, A local index theorem for non-Kähler manifolds, Holomorphic Morse inequalities for orbifolds, Analytic torsion forms for fibrations by projective curves, Localization and diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories, Complex equivariant intersection, excess normal bundles and Bott-Chern currents, On certain infinite dimensional aspects of Arakelov intersection theory, A fixed point formula of Lefschetz type in Arakelov geometry. I: Statement and proof, Koszul Complexes, Harmonic Oscillators, and the Todd Class, Equivariant Kähler geometry and localization in the \(G/G\) model, An equivariant version of the \(K\)-energy

Cites Work

• Unnamed Item
• The Atiyah-Singer theorems: A probabilistic approach. I: The index theorem
• Zeros d'un champ de vecteurs et classes characteristiques équivariantes
• Index theorem and equivariant cohomology on the loop space
• Localization formulas, superconnections, and the index theorem for families
• Determinants of Cauchy-Riemann operators on a Riemann surface
• 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
• A local index theorem for non-Kähler manifolds
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Harmonic spinors
• Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic section
• Curvature and the eigenforms of the Laplace operator
• An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds
• On the heat equation and the index theorem
• Curvature and the eigenvalues of the Laplacian for elliptic complexes
• Analytic torsion for complex manifolds