“Braids, Links, and Mapping Class Groups”
E628633
“Braids, Links, and Mapping Class Groups” is a foundational monograph in low-dimensional topology that systematically develops the theory of braids, links, and mapping class groups and their interrelations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| “Braids, Links, and Mapping Class Groups” canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6939315 — 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: “Braids, Links, and Mapping Class Groups” Context triple: [Joan S. Birman, notablePublication, “Braids, Links, and Mapping Class Groups”]
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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.
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B.
Foliations of Three-Manifolds Which Are Circle Bundles
"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.
-
C.
Dehn’s decision problems in group theory
Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
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D.
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.
-
E.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
- 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: “Braids, Links, and Mapping Class Groups” Target entity description: “Braids, Links, and Mapping Class Groups” is a foundational monograph in low-dimensional topology that systematically develops the theory of braids, links, and mapping class groups and their interrelations.
-
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.
Foliations of Three-Manifolds Which Are Circle Bundles
"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.
-
C.
Dehn’s decision problems in group theory
Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
-
D.
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.
-
E.
Thurston’s classification of surface diffeomorphisms
Thurston’s classification of surface diffeomorphisms is a foundational theorem in low-dimensional topology that categorizes self-maps of surfaces into periodic, reducible, or pseudo-Anosov types, profoundly influencing the study of 3-manifolds and dynamical systems.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ nonfiction book ⓘ |
| aim | to systematically develop the theory of braids, links, and mapping class groups and their interrelations ⓘ |
| author | Joan S. Birman NERFINISHED ⓘ |
| countryOfPublication |
United States of America
ⓘ
surface form:
United States
|
| field |
braid theory
ⓘ
geometric topology ⓘ knot theory ⓘ low-dimensional topology ⓘ mapping class groups ⓘ |
| hasPart |
appendices with technical results
ⓘ
chapter on braid groups ⓘ chapter on links and closed braids ⓘ chapter on mapping class groups ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in topology ⓘ |
| language | English ⓘ |
| notableFor |
foundational treatment of braid groups and their relation to links
ⓘ
systematic exposition of mapping class groups ⓘ |
| publicationYear | 1974 ⓘ |
| publisher | Princeton University Press NERFINISHED ⓘ |
| series | Annals of Mathematics Studies NERFINISHED ⓘ |
| subject |
3-manifolds
ⓘ
Alexander theorem ⓘ Artin braid group NERFINISHED ⓘ Dehn twists ⓘ Heegaard splittings NERFINISHED ⓘ Markov theorem NERFINISHED ⓘ Seifert surfaces ⓘ algebraic topology methods in knot theory ⓘ braid groups ⓘ closed braids ⓘ configuration spaces ⓘ covering spaces ⓘ fibered links ⓘ fundamental groups ⓘ isotopy classes of homeomorphisms ⓘ links in 3-manifolds ⓘ mapping class group actions ⓘ mapping class group of a surface ⓘ monodromy of fibered links ⓘ presentation of braid groups ⓘ representations of braid groups ⓘ surface homeomorphisms ⓘ |
| usedAs |
graduate-level textbook in topology courses
ⓘ
reference in low-dimensional 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: “Braids, Links, and Mapping Class Groups” Description of subject: “Braids, Links, and Mapping Class Groups” is a foundational monograph in low-dimensional topology that systematically develops the theory of braids, links, and mapping class groups and their interrelations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.