A Direct Geometric Proof of the Lefschetz Fixed Point Formulas

DOI10.2307/2153952zbMath0747.58016OpenAlexW4241366832MaRDI QIDQ3989198

Weiping Zhang, Yan Lin Yu, John D. Lafferty

Publication date: 28 June 1992

Full work available at URL: https://doi.org/10.2307/2153952

zbMATH Keywords

Lefschetz fixed point formula

Mathematics Subject Classification ID

Fixed-point theorems on manifolds (58C30) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Local Riemannian geometry (53B20) Differential invariants (local theory), geometric objects (53A55)

Related Items

Noncommutative geometry and conformal geometry. II: Connes-Chern character and the local equivariant index theorem ⋮ The noncommutative infinitesimal equivariant index formula. II. ⋮ The noncommutative family Atiyah-Patodi-Singer index theorem ⋮ The equivariant noncommutative Atiyah-Patodi-Singer index theorem ⋮ The \(L^2\)-Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities: a heat kernel approach ⋮ The equivariant Dirac cyclic cocycle ⋮ Trigonometry (II) ⋮ The mathematical work of V. K. Patodi ⋮ The equivariant family index theorem in odd dimensions

Cites Work

• The Atiyah-Singer theorems: A probabilistic approach. II: The Lefschetz fixed point formulas
• A short proof of the local Atiyah-Singer index theorem
• Proof of character-valued index theorems
• A Lefschetz fixed point formula for elliptic complexes. I
• A Lefschetz fixed point formula for elliptic complexes. II: Applications
• Curvature and the eigenforms of the Laplace operator
• An analytic proof of Riemann-Roch-Hirzebruch theorem for Kaehler manifolds
• A computation of the equivariant index of the Dirac operator
• Local index theorem for Dirac operator