Noncommutative Geometry (1994 book)
E286303
Noncommutative Geometry (1994 book) is Alain Connes’ foundational monograph that systematically develops the theory of noncommutative spaces and its applications to mathematics and theoretical physics.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Noncommutative Geometry (1994 book) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2648176 — 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: Noncommutative Geometry (1994 book) Context triple: [Alain Connes, notableWork, Noncommutative Geometry (1994 book)]
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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.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
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C.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
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D.
Introduction to Algebraic K-Theory
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
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E.
The Pisa Lectures
The Pisa Lectures are a series of influential talks by Noam Chomsky that laid out the core ideas of his Government and Binding theory in generative grammar.
- 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: Noncommutative Geometry (1994 book) Target entity description: Noncommutative Geometry (1994 book) is Alain Connes’ foundational monograph that systematically develops the theory of noncommutative spaces and its applications to mathematics and theoretical physics.
-
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.
Categories for the Working Mathematician
Categories for the Working Mathematician is a foundational textbook in category theory that systematically develops the subject and its applications for professional mathematicians.
-
C.
“K-Theory” (book with Friedrich Hirzebruch and others)
“K-Theory” is a foundational mathematical monograph co-authored by Michael Atiyah, Friedrich Hirzebruch, and others that systematically develops topological K-theory and its applications in geometry and topology.
-
D.
Introduction to Algebraic K-Theory
Introduction to Algebraic K-Theory is a foundational graduate-level textbook by John Milnor that systematically develops the basic concepts and techniques of algebraic K-theory in a concise and influential style.
-
E.
The Pisa Lectures
The Pisa Lectures are a series of influential talks by Noam Chomsky that laid out the core ideas of his Government and Binding theory in generative grammar.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics monograph
ⓘ
non-fiction book ⓘ |
| author | Alain Connes ⓘ |
| field |
functional analysis
ⓘ
mathematical physics ⓘ noncommutative geometry ⓘ operator algebras ⓘ |
| genre |
advanced mathematics textbook
ⓘ
research monograph ⓘ |
| hasMainConcept |
duality between spaces and commutative C*-algebras
ⓘ
extension of geometric notions to noncommutative algebras ⓘ noncommutative space as an operator algebra ⓘ use of spectral data to encode geometry ⓘ |
| influenced |
development of spectral action models in physics
ⓘ
research in index theory ⓘ research in mathematical formulations of the Standard Model ⓘ research in operator algebras ⓘ |
| language | English ⓘ |
| notableFor |
applications of noncommutative geometry to physics
ⓘ
foundational exposition of spectral triples ⓘ introduction of cyclic cohomology as a tool in noncommutative geometry ⓘ systematic development of noncommutative geometry ⓘ |
| publicationYear | 1994 ⓘ |
| subject |
C*-algebras
ⓘ
Chern character ⓘ
surface form:
Chern character in cyclic cohomology
Dirac operator ⓘ
surface form:
Dirac operators
Fredholm modules ⓘ K-theory ⓘ applications to gauge theory ⓘ applications to gravity ⓘ applications to particle physics ⓘ applications to the Standard Model of particle physics ⓘ cyclic cohomology ⓘ foliation C*-algebras ⓘ index theory ⓘ leaf spaces of foliations ⓘ local index formula ⓘ measure theory on noncommutative spaces ⓘ noncommutative integration ⓘ noncommutative spaces ⓘ noncommutative tori ⓘ quantum groups ⓘ spectral action principle ⓘ spectral triples ⓘ transverse geometry of foliations ⓘ von Neumann algebras ⓘ |
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: Noncommutative Geometry (1994 book) Description of subject: Noncommutative Geometry (1994 book) is Alain Connes’ foundational monograph that systematically develops the theory of noncommutative spaces and its applications to mathematics and theoretical physics.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.