“K-Theory” (book with Friedrich Hirzebruch and others)
E255577
“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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “K-Theory” (book with Friedrich Hirzebruch and others) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2314514 — 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: “K-Theory” (book with Friedrich Hirzebruch and others) Context triple: [Michael Atiyah, notableWork, “K-Theory” (book with Friedrich Hirzebruch and others)]
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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.
-
B.
Grothendieck–Riemann–Roch theorem
The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
-
C.
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.
-
D.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
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E.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
- 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: “K-Theory” (book with Friedrich Hirzebruch and others) Target entity description: “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.
-
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.
Grothendieck–Riemann–Roch theorem
The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
-
C.
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.
-
D.
Chern classes
Chern classes are fundamental topological invariants in differential and algebraic geometry that classify complex vector bundles and capture their curvature and twisting properties.
-
E.
Grothendieck group
The Grothendieck group is an algebraic construction that formally turns a commutative monoid (often arising from isomorphism classes of objects like vector bundles or modules) into an abelian group, playing a central role in K-theory and modern algebraic geometry.
- F. None of above. chosen
Statements (32)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| aboutConcept |
Bott periodicity
ⓘ
Chern character ⓘ applications to manifold theory ⓘ characteristic classes ⓘ cohomology theories ⓘ generalized cohomology ⓘ homotopy theory ⓘ index theory ⓘ operator K-theory ⓘ vector bundles ⓘ |
| describes |
applications of K-theory in geometry
ⓘ
applications of K-theory in topology ⓘ |
| develops | foundations of topological K-theory ⓘ |
| fieldOfStudy | mathematics ⓘ |
| hasAuthor |
Friedrich Hirzebruch
ⓘ
Michael Atiyah ⓘ other mathematicians ⓘ |
| hasDiscipline |
algebraic topology
ⓘ
differential geometry ⓘ global analysis ⓘ |
| hasGenre |
mathematics textbook
ⓘ
research monograph ⓘ |
| hasLanguage | English ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| mainSubject |
algebraic topology
ⓘ
geometry ⓘ topological K-theory ⓘ topology ⓘ |
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: “K-Theory” (book with Friedrich Hirzebruch and others) Description of subject: “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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.