Michael Atiyah’s work in algebraic topology
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Publication:5165434
DOI10.1090/bull/1746zbMath1480.01056OpenAlexW3185032677MaRDI QIDQ5165434
Publication date: 16 November 2021
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/bull/1746
Biographies, obituaries, personalia, bibliographies (01A70) History of algebraic topology (55-03) History of global analysis (58-03) History of (K)-theory (19-03)
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Cites Work
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- A Fourier-Mukai approach to the \(K\)-theory of compact Lie groups
- Homotopiemengen und ihre induzierten Abbildungen. I.-II.: Sphärenähnliche Mannigfaltigkeiten
- Homogeneous vector bundles
- On the non-existence of elements of Hopf invariant one
- Characters and cohomology of finite groups
- An analytic proof of Novikov's theorem on rational Pontrjagin classes
- Analytic cycles on complex manifolds
- The Riemann-Roch theorem for analytic embeddings
- Cohomologie-Operationen und charakteristische Klassen. (Cohomology operations and characteristic classes)
- Immersions and embeddings of manifolds
- The transfer map and fiber bundles
- On a theorem of Pittie
- Extensions of \(C^*\)-algebras and \(K\)-homology
- The local index formula in noncommutative geometry
- A topological proof of the Bott periodicity theorems
- On the periodicity theorem for complex vector bundles
- Clifford modules
- Group representations, \(\lambda\)-rings and the \(J\)-homomorphism
- On the K-theory of Lie groups
- Elementary proofs of some results of cobordism theory using Steenrod operations
- Equivariant \(K\)-theory and completion
- The mod 2 cohomology rings of extra-special 2-groups and the spinor groups
- The spectrum of an equivariant cohomology ring. I. II
- Novikov's higher signature and families of elliptic operators
- On the groups \(J(X)\). I
- Complex Analytic Connections in Fibre Bundles
- On the parallelizability of the spheres
- Vector Bundles Over an Elliptic Curve
- Spaces Associated with Stiefel Manifolds
- Le théorème de Riemann-Roch
- Seminar on Transformation Groups. (AM-46)
- Characteristic Classes and Homogeneous Spaces, I
- Characteristic Classes. (AM-76)
- Atiyah’s work on holomorphic vector bundles and gauge theories
- The Atiyah–Singer index theorem
- Thom Complexes
- K-THEORY AND THE HOPF INVARIANT
- Riemann-Roch theorems for differentiable manifolds
- POWER OPERATIONS IN K-THEORY
- BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
- K-THEORY INVARIANTS FOR UNITARY G-BORDISM
- On Steenrod's Reduced Powers, the Index of Inertia, and the Todd Genus
- Track Groups (I)
- Vector fields on spheres