The infinitesimal Lefschetz formulas: A heat equation proof

DOI10.1016/0022-1236(85)90013-8zbMath0572.58021OpenAlexW2074424959MaRDI QIDQ1062332

Jean-Michel Bismut

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0022-1236(85)90013-8

zbMATH Keywords

Dirac operatorLefschetz formulashomotopyheat equation methods

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Topology of vector bundles and fiber bundles (57R22) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (14)

Localization formulas, superconnections, and the index theorem for families ⋮ The noncommutative infinitesimal equivariant index formula. II. ⋮ Transgressed Chern forms for Dirac operators ⋮ Demailly's asymptotic Morse inequalities: a heat equation proof ⋮ Multiplicities formula for geometric quantization. I ⋮ Comparison of two equivariant \(\eta\)-forms ⋮ The \(L^2\)-Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities: a heat kernel approach ⋮ Differential \(K\)-theory and localization formula for \(\eta \)-invariants ⋮ Atiyah-Bott-Lefschetz formula for elliptic complexes on manifolds with boundary ⋮ Koszul Complexes, Harmonic Oscillators, and the Todd Class ⋮ Unnamed Item ⋮ Differential \(K\)-theory, \(\eta\)-invariant, and localization ⋮ The Noncommutative Infinitesimal Equivariant Index Formula ⋮ The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs

Cites Work

• The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
• Large deviations and the Malliavin calculus
• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• Zeros d'un champ de vecteurs et classes characteristiques équivariantes
• The moment map and equivariant cohomology
• Index theorem and equivariant cohomology on the loop space
• Supersymmetry and Morse theory
• Addendum to ``On the variation in the cohomology of the symplectic form of the reduced phase space
• Vector fields and characteristic numbers
• The index of elliptic operators. II
• A Lefschetz fixed point formula for elliptic complexes. II: Applications
• The index of elliptic operators. IV, V
• The Equivariant Index and Kirillov's Character Formula
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