Kirby calculus
E911226
Kirby calculus is a set of moves and techniques in low-dimensional topology used to manipulate framed links in three-manifolds and study and classify four-manifolds.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Kirby calculus canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11214936 — 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: Kirby calculus Context triple: [Dehn surgery, relatedConcept, Kirby calculus]
-
A.
Kirby Krackle
Kirby Krackle is a distinctive comic book art technique characterized by clusters of black dots used to depict cosmic energy, explosions, and other powerful forces, most famously associated with artist Jack Kirby.
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B.
Kirby Building
The Kirby Building is a historic high-rise in downtown Dallas, Texas, known for its early 20th-century architecture and adaptive reuse as residential lofts.
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C.
City of Kirby
The City of Kirby is a small suburban municipality located within the San Antonio metropolitan area in Bexar County, Texas.
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D.
Kirby Keger
Kirby Keger is a lovestruck, ambitious young law student and bartender portrayed by Emilio Estevez in the 1985 coming-of-age film "St. Elmo's Fire."
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E.
Kirby Air Ride
Kirby Air Ride is a fast-paced racing game for the Nintendo GameCube featuring Kirby riding various warp stars across diverse courses, with simple controls and multiple multiplayer modes.
- 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: Kirby calculus Target entity description: Kirby calculus is a set of moves and techniques in low-dimensional topology used to manipulate framed links in three-manifolds and study and classify four-manifolds.
-
A.
Kirby Krackle
Kirby Krackle is a distinctive comic book art technique characterized by clusters of black dots used to depict cosmic energy, explosions, and other powerful forces, most famously associated with artist Jack Kirby.
-
B.
Kirby Building
The Kirby Building is a historic high-rise in downtown Dallas, Texas, known for its early 20th-century architecture and adaptive reuse as residential lofts.
-
C.
City of Kirby
The City of Kirby is a small suburban municipality located within the San Antonio metropolitan area in Bexar County, Texas.
-
D.
Kirby Keger
Kirby Keger is a lovestruck, ambitious young law student and bartender portrayed by Emilio Estevez in the 1985 coming-of-age film "St. Elmo's Fire."
-
E.
Kirby Air Ride
Kirby Air Ride is a fast-paced racing game for the Nintendo GameCube featuring Kirby riding various warp stars across diverse courses, with simple controls and multiple multiplayer modes.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theory
ⓘ
technique in low-dimensional topology ⓘ |
| appliesTo |
3-manifolds
ⓘ
4-manifolds ⓘ |
| basedOn | handle decompositions of manifolds ⓘ |
| characterizedBy | finite set of local moves on framed links ⓘ |
| concerns |
framing integers on link components
ⓘ
linking matrices ⓘ |
| coreConcept |
Kirby moves
ⓘ
framed links in S^3 ⓘ handlebody decompositions ⓘ |
| field | low-dimensional topology ⓘ |
| formalism | link diagrams with framings ⓘ |
| hasMove |
blow down
ⓘ
blow up ⓘ cancellation of handle pairs ⓘ destabilization ⓘ handle slide ⓘ introduction of cancelling handle pairs ⓘ stabilization ⓘ |
| hasTheorem | Kirby theorem ⓘ |
| helpsCompute | intersection form of a 4-manifold from a link diagram ⓘ |
| helpsConstruct | handle decompositions of 4-manifolds from framed links ⓘ |
| implies | two framed links related by Kirby moves yield homeomorphic 3-manifolds ⓘ |
| introducedBy | Robion Kirby ⓘ |
| Kirby theorem | equivalence of 3-manifolds via surgery corresponds to Kirby moves on framed links ⓘ |
| mathematicsSubjectClassification |
57M25
ⓘ
57R65 ⓘ |
| namedAfter | Robion Kirby ⓘ |
| relatedTo |
Fenn–Rourke moves
ⓘ
Morse theory ⓘ
linked to:
Morse Theory
Rolfsen moves ⓘ handle theory ⓘ surgery on links ⓘ |
| relates | framed links in S^3 and 3-manifolds obtained by surgery ⓘ |
| toolFor |
proving equivalence of 3-manifolds obtained by surgery
ⓘ
translating handle decompositions into link diagrams ⓘ |
| typicalAmbientSpace |
3-sphere S^3
ⓘ
linked to:
Hopf fibration
|
| usedBy | geometric topologists ⓘ |
| usedFor |
classifying four-manifolds
ⓘ
manipulating framed links in three-manifolds ⓘ studying four-manifolds ⓘ |
| usedIn |
Dehn surgery description of 3-manifolds
ⓘ
classification of simply connected smooth 4-manifolds ⓘ construction of exotic 4-manifolds ⓘ study of intersection forms of 4-manifolds ⓘ study of smooth structures on 4-manifolds ⓘ surgery 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: Kirby calculus Description of subject: Kirby calculus is a set of moves and techniques in low-dimensional topology used to manipulate framed links in three-manifolds and study and classify four-manifolds.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.