“Elliptic Operators and Compact Groups” (with Raoul Bott)
E255579
“Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “Elliptic Operators and Compact Groups” (with Raoul Bott) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2314516 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: “Elliptic Operators and Compact Groups” (with Raoul Bott) Context triple: [Michael Atiyah, notableWork, “Elliptic Operators and Compact Groups” (with Raoul Bott)]
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A.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
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B.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
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C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
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D.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
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E.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: “Elliptic Operators and Compact Groups” (with Raoul Bott) Target entity description: “Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
-
A.
Atiyah–Singer index theorem
The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
-
B.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
-
C.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
D.
The Poincaré-Birkhoff-Witt theorem in ring theory
"The Poincaré-Birkhoff-Witt theorem in ring theory" is a mathematical work, attributed here to N. G. de Bruijn, that studies and applies the Poincaré–Birkhoff–Witt theorem in the context of associative and Lie-theoretic ring structures.
-
E.
Produits tensoriels topologiques et espaces nucléaires
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf | mathematics research paper ⓘ |
| author |
Michael Atiyah
ⓘ
Raoul Bott ⓘ |
| context |
development of the Atiyah–Singer index theorem
ⓘ
study of elliptic operators on manifolds with symmetry ⓘ |
| contribution |
developed the theory of equivariant index for elliptic operators
ⓘ
extended index theory to manifolds with compact Lie group actions ⓘ related equivariant indices to characters of group representations ⓘ |
| field | mathematics ⓘ |
| hasKeyConcept |
G-equivariant elliptic operator
ⓘ
K-theoretic formulation of index ⓘ character of a representation ⓘ equivariant K-theory of a G-space ⓘ equivariant index map ⓘ fixed point contribution of group elements ⓘ localization at fixed points ⓘ |
| hasKeyResult |
compatibility of equivariant index with induction and restriction of group actions
ⓘ
formula expressing equivariant index as a sum of fixed point contributions ⓘ functorial properties of the equivariant index ⓘ identification of equivariant index with a virtual representation of the group ⓘ |
| impact |
bridged index theory and representation theory
ⓘ
influenced subsequent research on localization formulas in equivariant cohomology ⓘ provided foundational tools for later work in equivariant index theory ⓘ |
| influenced |
equivariant K-theory
ⓘ
geometric representation theory ⓘ modern index theory ⓘ representation theory of compact Lie groups ⓘ topological aspects of quantum field theory ⓘ |
| language | English ⓘ |
| subfield |
differential geometry
ⓘ
equivariant K-theory ⓘ global analysis ⓘ index theory ⓘ representation theory ⓘ |
| topic |
Atiyah–Singer index theorem
ⓘ
compact Lie group actions ⓘ elliptic differential operators ⓘ equivariant elliptic operators ⓘ equivariant index ⓘ fixed point formulas ⓘ |
| uses |
compact Lie group representation theory
ⓘ
differential topology ⓘ functional analysis ⓘ topological K-theory ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: “Elliptic Operators and Compact Groups” (with Raoul Bott) Description of subject: “Elliptic Operators and Compact Groups” (with Raoul Bott) is a seminal mathematical paper that develops the theory of equivariant index for elliptic operators under compact Lie group actions, laying key foundations for modern index theory and representation theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.