The Index of Elliptic Operators: I

1968/05/01 by M. F. Atiyah, Michael Atiyah, I. M. Singer · 23 citations
Mathematics · #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics

paper · doi:10.2307/1970715

crossref issued 1968/05/01 · crossref published 1968/05/01 · crossref published-print 1968/05/01 · openalex publication_date 1968/05/01 · crossref created 2006/04/24 · crossref deposited 2018/05/09 · openalex created_date 2025/10/10 · crossref indexed 2026/07/07 · openalex updated_date 2026/07/15

Citations

• The index of elliptic operators on compact manifolds

Cited by

• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Numerical study of the lattice index theorem using improved cooling and overlap fermions
• Sir Michael Atiyah, a Knight Mathematician
• Lecture Notes on Normalizing Flows for Lattice Quantum Field Theories
• Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes
• Supersymmetry and Morse theory
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• TOPOLOGICAL INVARIANTS OF ELLIPTIC OPERATORS. I:K-HOMOLOGY
• Quasiconformal 4-manifolds
• Positive scalar curvature and the Dirac operator on complete riemannian manifolds
• The index of signature operators on Lipschitz manifolds
• The Atiyah—Singer theorems: A probabilistic approach. I. The index theorem
• Transversality and the index theorem
• Electric-magnetic duality and the geometric Langlands program
• Gravitation, gauge theories and differential geometry
• The periodicity theorem for the classical groups and some of its applications
• K-Theory of pseudodifferential operators with semi-periodic symbols
• René Thom’s work on geometric homology and bordism
• An instanton-invariant for 3-manifolds
• Symplectic fixed points and holomorphic spheres
• Atiyah–Singer index theorem [wikipedia]
• Michael Atiyah [wikipedia]
• Pseudo-differential operator [wikipedia]