"Algebraic Topology"
E305928
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
All labels observed (1)
| Label | Occurrences |
|---|---|
| "Algebraic Topology" canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2866512 — 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: "Algebraic Topology" Context triple: [Princeton Mathematical Series, workIncluded, "Algebraic Topology"]
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
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B.
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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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.
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D.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
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E.
“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.
- 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: "Algebraic Topology" Target entity description: "Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
A.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
B.
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.
-
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.
Moscow school of topology
The Moscow school of topology was a prominent mathematical tradition centered in Moscow that made foundational contributions to general and algebraic topology in the 20th century.
-
E.
“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.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
foundational text in topology
ⓘ
mathematics textbook ⓘ reference work in algebraic topology ⓘ |
| appliesTo |
CW-complexes
ⓘ
manifolds ⓘ topological spaces ⓘ |
| approach | assign algebraic invariants to topological spaces ⓘ |
| coversTopic |
algebraic invariants of manifolds
ⓘ
cell complexes and CW-complexes ⓘ cohomology theory ⓘ duality theorems in topology ⓘ exact sequences in homology ⓘ fundamental group and covering spaces ⓘ homology theory ⓘ homotopy theory ⓘ |
| developsConcept |
CW-complexes
ⓘ
Eilenberg–Steenrod axioms ⓘ Künneth formula ⓘ Mayer–Vietoris sequence in de Rham cohomology ⓘ
surface form:
Mayer–Vietoris sequence
Poincaré duality ⓘ cellular homology ⓘ cohomology groups ⓘ covering spaces ⓘ exact sequences ⓘ fundamental group ⓘ homology groups ⓘ simplicial complexes ⓘ singular homology ⓘ topological invariants ⓘ universal coefficient theorem ⓘ |
| field | algebraic topology ⓘ |
| goal |
classify topological spaces up to homeomorphism
ⓘ
classify topological spaces up to homotopy equivalence ⓘ |
| language | English ⓘ |
| subjectArea |
algebra
ⓘ
topology ⓘ |
| typicalAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ research mathematicians in topology ⓘ |
| usesMethod |
algebraic methods in topology
ⓘ
cohomology theory ⓘ homology theory ⓘ |
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: "Algebraic Topology" Description of subject: "Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.