Bismut’s local families index theorem
E1197990
UNEXPLORED
Bismut’s local families index theorem is a refinement of the Atiyah–Singer families index theorem that expresses the family index in terms of local differential-geometric data using superconnection techniques.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bismut’s local families index theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T16151014 — 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: Bismut’s local families index theorem Context triple: [families index theorem, influenced, Bismut’s local families index theorem]
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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.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
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C.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
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D.
equivariant index theorem
The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.
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E.
Hirzebruch signature theorem
The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
- 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: Bismut’s local families index theorem Target entity description: Bismut’s local families index theorem is a refinement of the Atiyah–Singer families index theorem that expresses the family index in terms of local differential-geometric data using superconnection techniques.
-
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.
Atiyah–Bott fixed-point theorem
The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
-
C.
Connes–Moscovici index theorem
The Connes–Moscovici index theorem is a fundamental result in noncommutative geometry that generalizes the classical Atiyah–Singer index theorem to the setting of foliations and noncommutative spaces.
-
D.
equivariant index theorem
The equivariant index theorem is a generalization of the Atiyah–Singer index theorem that computes indices of elliptic operators while taking into account the action of a symmetry group.
-
E.
Hirzebruch signature theorem
The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.