Michael Atiyah’s work in algebraic topology

DOI10.1090/bull/1746zbMath1480.01056OpenAlexW3185032677MaRDI QIDQ5165434

Graeme B. Segal

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

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) History of algebraic topology (55-03) History of global analysis (58-03) History of (K)-theory (19-03)

Related Items

Introduction to the Atiyah issue, The Atiyah–Singer index theorem

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