Todd class
E391905
The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Todd class canonical | 6 |
How this entity was disambiguated
This entity first appeared as the object of triple T3821388 — 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: Todd class Context triple: [Atiyah–Singer index theorem, usesConcept, Todd class]
-
A.
Y class
Y class is the standard economy fare class used by airlines, typically representing full-fare economy tickets with the least restrictions on changes and refunds.
-
B.
Klas
Klas is a Scandinavian given name, commonly used as a variant of Nicholas.
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C.
Tucker
Tucker is a surname most notably associated with Albert W. Tucker, a Canadian-American mathematician and game theorist known for his contributions to topology and the formalization of the prisoner's dilemma.
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D.
Schull
Schull is a small coastal village and popular tourist destination on the Mizen Peninsula in West County Cork, Ireland.
-
E.
Tri-C
Tri-C is a large public community college in Cuyahoga County, Ohio, offering a wide range of associate degrees, certificates, and workforce training programs.
- 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: Todd class Target entity description: The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
-
A.
Y class
Y class is the standard economy fare class used by airlines, typically representing full-fare economy tickets with the least restrictions on changes and refunds.
-
B.
Klas
Klas is a Scandinavian given name, commonly used as a variant of Nicholas.
-
C.
Tucker
Tucker is a surname most notably associated with Albert W. Tucker, a Canadian-American mathematician and game theorist known for his contributions to topology and the formalization of the prisoner's dilemma.
-
D.
Schull
Schull is a small coastal village and popular tourist destination on the Mizen Peninsula in West County Cork, Ireland.
-
E.
Tri-C
Tri-C is a large public community college in Cuyahoga County, Ohio, offering a wide range of associate degrees, certificates, and workforce training programs.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
characteristic class
ⓘ
cohomology class ⓘ topological invariant ⓘ |
| appearsAsFactorIn |
Grothendieck–Riemann–Roch theorem
ⓘ
surface form:
Grothendieck–Riemann–Roch integrand
|
| appearsIn |
Riemann–Roch theorem
ⓘ
surface form:
Riemann–Roch formulas
characteristic class formulas ⓘ |
| appliesTo |
complex manifold
ⓘ
complex vector bundle ⓘ holomorphic vector bundle ⓘ |
| associatedWith | Chern character ⓘ |
| constructedFrom | Chern classes ⓘ |
| definedFor | complex line bundle ⓘ |
| definedOn | cohomology ring ⓘ |
| degreeZeroComponent | 1 ⓘ |
| dependsOn | Chern roots ⓘ |
| domain |
algebraic K-theory
ⓘ
complex K-theory ⓘ |
| encodes | curvature information ⓘ |
| field |
algebraic geometry
ⓘ
complex geometry ⓘ differential geometry ⓘ topology ⓘ |
| generalizes | Todd genus ⓘ |
| is |
multiplicative characteristic class
ⓘ
rational characteristic class ⓘ |
| isExampleOf | multiplicative sequence of polynomials in Chern classes ⓘ |
| isFunctorialFor | holomorphic maps ⓘ |
| isInvariantUnder | holomorphic isomorphisms ⓘ |
| namedAfter |
John Todd
ⓘ
surface form:
John Arthur Todd
|
| relatedTo |
Chern classes
ⓘ
Pontryagin classes ⓘ Â-genus ⓘ |
| roleIn |
Atiyah–Singer index theorem
ⓘ
Grothendieck–Riemann–Roch theorem ⓘ Hirzebruch–Riemann–Roch theorem ⓘ index theorem ⓘ |
| takesValuesIn | rational cohomology ⓘ |
| usedIn |
birational geometry
ⓘ
enumerative geometry ⓘ intersection theory ⓘ theory of algebraic varieties ⓘ theory of complex manifolds ⓘ |
| usedToCompute |
holomorphic Euler characteristic
ⓘ
indices of elliptic operators ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Todd class Description of subject: The Todd class is a characteristic class in complex geometry and topology that plays a central role in index theorems by encoding curvature information of complex vector bundles.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.