John Milnor's book "Lectures on the h-Cobordism Theorem"
E911351
John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| John Milnor's book "Lectures on the h-Cobordism Theorem" canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11219253 — 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: John Milnor's book "Lectures on the h-Cobordism Theorem" Context triple: [h-cobordism theorem, standardReference, John Milnor's book "Lectures on the h-Cobordism Theorem"]
-
A.
M. Hirsch, Differential Topology
*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.
-
B.
J. Munkres, Elementary Differential Topology
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
C.
h-cobordism theorem
The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
-
D.
Thom cobordism theory
Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
-
E.
Classifying Spaces and Fibrations
"Classifying Spaces and Fibrations" is a mathematical work that develops the theory of classifying spaces in algebraic topology and their relationship to fiber bundles and fibrations.
- 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: John Milnor's book "Lectures on the h-Cobordism Theorem" Target entity description: John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
-
A.
M. Hirsch, Differential Topology
*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.
-
B.
J. Munkres, Elementary Differential Topology
"J. Munkres, Elementary Differential Topology" is a classic introductory textbook that rigorously develops the foundations of differential topology, including topics such as smooth manifolds, transversality, and approximation theorems.
-
C.
h-cobordism theorem
The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
-
D.
Thom cobordism theory
Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
-
E.
Classifying Spaces and Fibrations
"Classifying Spaces and Fibrations" is a mathematical work that develops the theory of classifying spaces in algebraic topology and their relationship to fiber bundles and fibrations.
- F. None of above. chosen
Statements (34)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| author | John Milnor NERFINISHED ⓘ |
| basedOn | lectures by John Milnor ⓘ |
| contains |
applications of the h-cobordism theorem
ⓘ
proof of the h-cobordism theorem ⓘ |
| countryOfPublication |
United States of America
ⓘ
surface form:
United States
|
| field | differential topology ⓘ |
| focusesOn | classification of high-dimensional manifolds ⓘ |
| format | print ⓘ |
| hasAuthor | John Milnor NERFINISHED ⓘ |
| influenced |
study of high-dimensional manifold topology
ⓘ
surgery theory in topology ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in topology ⓘ |
| isClassicIn | differential topology literature ⓘ |
| language | English ⓘ |
| length | short monograph ⓘ |
| mainTopic |
cobordism theory
ⓘ
h-cobordism theorem NERFINISHED ⓘ high-dimensional manifolds ⓘ |
| notableFor |
clarity of exposition
ⓘ
influence on differential topology ⓘ |
| originalPublicationYear | 1965 ⓘ |
| provides | rigorous exposition of the h-cobordism theorem ⓘ |
| publisher | Princeton University Press NERFINISHED ⓘ |
| relatedTo |
Poincaré conjecture in high dimensions
ⓘ
s-cobordism theorem ⓘ |
| series | Princeton Mathematical Notes NERFINISHED ⓘ |
| subjectArea |
geometry
ⓘ
topology ⓘ |
| uses |
handlebody decompositions
ⓘ
techniques from Morse 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: John Milnor's book "Lectures on the h-Cobordism Theorem" Description of subject: John Milnor's "Lectures on the h-Cobordism Theorem" is a classic monograph in differential topology that gives a clear, rigorous exposition of the h-cobordism theorem and its applications to the classification of high-dimensional manifolds.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
h-cobordism theorem
→
standardReference
→
John Milnor's book "Lectures on the h-Cobordism Theorem"
ⓘ