Foliations of Three-Manifolds Which Are Circle Bundles
E518461
"Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Foliations of Three-Manifolds Which Are Circle Bundles canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5425329 — 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: Foliations of Three-Manifolds Which Are Circle Bundles Context triple: [William Thurston, doctoralThesisTitle, Foliations of Three-Manifolds Which Are Circle Bundles]
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A.
Wirtinger presentation of knot groups
The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
-
B.
Dehn surgery
Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
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C.
Hyperbolic Manifolds and Discrete Groups
"Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
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D.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
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E.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
- 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: Foliations of Three-Manifolds Which Are Circle Bundles Target entity description: "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
-
A.
Wirtinger presentation of knot groups
The Wirtinger presentation of knot groups is a classical method in knot theory that describes the fundamental group of a knot complement using generators and relations derived from a knot diagram.
-
B.
Dehn surgery
Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
-
C.
Hyperbolic Manifolds and Discrete Groups
"Hyperbolic Manifolds and Discrete Groups" is a foundational mathematical monograph that develops the theory of hyperbolic geometry and its deep connections with discrete group actions and low-dimensional topology.
-
D.
Thom–Mather stratification
Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
-
E.
Milnor fibration
Milnor fibration is a fundamental construction in singularity theory and differential topology that describes how the complement of a complex hypersurface singularity fibers over the circle, revealing the local topological structure of the singularity.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
doctoral dissertation
ⓘ
mathematician ⓘ mathematics dissertation ⓘ work in geometric topology ⓘ |
| academicDegree | PhD ⓘ |
| academicStatus | unpublished dissertation manuscript ⓘ |
| advisor |
Morris W. Hirsch
ⓘ
linked to:
Morris Hirsch
|
| associatedConcept |
Seifert fibered 3-manifolds
ⓘ
surface bundles and circle bundles ⓘ |
| author |
William P. Thurston
ⓘ
linked to:
William Thurston
|
| authorInstanceOf |
William P. Thurston
ⓘ
linked to:
William Thurston
|
| contribution |
clarified the structure of foliations transverse to circle fibers
ⓘ
developed classification results for foliations on circle bundles over surfaces ⓘ influenced later work on 3-manifold topology and geometry ⓘ introduced influential techniques for studying foliations on 3-manifolds ⓘ |
| countryOfOrigin |
United States
ⓘ
linked to:
United States of America
|
| field |
3-manifold topology
ⓘ
foliation theory ⓘ geometric topology ⓘ |
| genre | research thesis ⓘ |
| hasPart |
classification results for foliations on circle bundles
ⓘ
examples and constructions of foliations on 3-manifolds ⓘ introduction to foliations on 3-manifolds ⓘ |
| impact | considered an early foundational work of Thurston in 3-manifold theory ⓘ |
| influenced |
development of Thurston’s later work on 3-manifolds
ⓘ
subsequent research in foliation theory ⓘ |
| institution | University of California, Berkeley ⓘ |
| language | English ⓘ |
| relatedTo |
Reeb components in foliations
ⓘ
Seifert fiber space theory ⓘ Thurston’s later geometrization ideas ⓘ taut foliations on 3-manifolds ⓘ |
| supervisingInstitution |
Department of Mathematics, University of California, Berkeley
ⓘ
linked to:
Department of Mathematics (UC Berkeley)
|
| timePeriod | 20th-century mathematics ⓘ |
| topic |
Reebless foliations
ⓘ
circle bundles over surfaces ⓘ classification of foliations on Seifert fibered spaces ⓘ codimension-one foliations ⓘ foliations of 3-manifolds ⓘ taut foliations ⓘ topology of 3-manifolds that are circle bundles over surfaces ⓘ |
| yearCompleted | 1972 ⓘ |
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Input
Subject: Foliations of Three-Manifolds Which Are Circle Bundles Description of subject: "Foliations of Three-Manifolds Which Are Circle Bundles" is William Thurston’s influential 1972 doctoral dissertation in geometric topology, where he developed foundational ideas about the structure and classification of foliations on 3-manifolds.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.