M. Hirsch, Differential Topology
E285920
*Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
All labels observed (1)
| Label | Occurrences |
|---|---|
| M. Hirsch, Differential Topology canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2652955 — 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: M. Hirsch, Differential Topology Context triple: [Whitney approximation theorem, standardReference, M. Hirsch, Differential Topology]
-
A.
Stephen Smale
Stephen Smale is an American mathematician renowned for his work in topology, dynamical systems, and mathematical economics, and as a recipient of the Fields Medal.
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B.
René Thom
René Thom was a French mathematician renowned for developing catastrophe theory and making fundamental contributions to topology, for which he received the Fields Medal.
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C.
John Milnor
John Milnor is an American mathematician renowned for his groundbreaking work in differential topology, K-theory, and dynamical systems, and is one of the most influential figures in modern mathematics.
-
D.
Dusa McDuff
Dusa McDuff is a prominent British-American mathematician renowned for her foundational contributions to symplectic geometry and topology.
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E.
Isadore Singer
Isadore Singer was an American mathematician renowned for co-formulating the Atiyah–Singer Index Theorem, a foundational result linking analysis, topology, and 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: M. Hirsch, Differential Topology Target entity description: *Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
-
A.
Stephen Smale
Stephen Smale is an American mathematician renowned for his work in topology, dynamical systems, and mathematical economics, and as a recipient of the Fields Medal.
-
B.
René Thom
René Thom was a French mathematician renowned for developing catastrophe theory and making fundamental contributions to topology, for which he received the Fields Medal.
-
C.
John Milnor
John Milnor is an American mathematician renowned for his groundbreaking work in differential topology, K-theory, and dynamical systems, and is one of the most influential figures in modern mathematics.
-
D.
Dusa McDuff
Dusa McDuff is a prominent British-American mathematician renowned for her foundational contributions to symplectic geometry and topology.
-
E.
Isadore Singer
Isadore Singer was an American mathematician renowned for co-formulating the Atiyah–Singer Index Theorem, a foundational result linking analysis, topology, and geometry.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
graduate-level textbook
ⓘ
mathematics textbook ⓘ reference work ⓘ |
| abbreviation | GTM 33 ⓘ |
| audience |
graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| author |
M. Hirsch
ⓘ
linked to:
Morris Hirsch
Morris W. Hirsch ⓘ
linked to:
Morris Hirsch
|
| field |
differential geometry
ⓘ
differential topology ⓘ topology ⓘ |
| language | English ⓘ |
| level | advanced ⓘ |
| prerequisite |
advanced calculus
ⓘ
basic differential geometry ⓘ point-set topology ⓘ |
| publisher | Springer ⓘ |
| reputation |
classic text in differential topology
ⓘ
standard reference in differential topology ⓘ |
| series | Graduate Texts in Mathematics ⓘ |
| topic |
Morse functions
ⓘ
Sard's theorem ⓘ Thom transversality theorem ⓘ Whitney approximation theorem ⓘ Whitney embedding theorem ⓘ cobordism ⓘ degree theory ⓘ embedding theorems ⓘ flows ⓘ handle decompositions ⓘ homotopy ⓘ immersion theorems ⓘ implicit function theorem ⓘ intersection theory ⓘ isotopy ⓘ manifolds with boundary ⓘ orientation of manifolds ⓘ regular values ⓘ smooth manifolds ⓘ smooth maps ⓘ submanifolds ⓘ submersions ⓘ tangent bundles ⓘ transversality ⓘ vector bundles ⓘ vector fields ⓘ |
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: M. Hirsch, Differential Topology Description of subject: *Differential Topology* by M. Hirsch is a classic graduate-level textbook that systematically develops the foundations of differential topology and is widely regarded as a standard reference in the field.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.