Witten–Reshetikhin–Turaev invariant
E508543
The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Reshetikhin–Turaev invariants | 1 |
| Witten–Reshetikhin–Turaev invariant canonical | 1 |
| Witten–Reshetikhin–Turaev invariants | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5273893 — 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: Witten–Reshetikhin–Turaev invariant Context triple: [topological quantum field theory, producesInvariant, Witten–Reshetikhin–Turaev invariant]
-
A.
Jones polynomial
The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
-
B.
HOMFLY-PT polynomial
The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
-
C.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
-
D.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
-
E.
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.
- 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: Witten–Reshetikhin–Turaev invariant Target entity description: The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
-
A.
Jones polynomial
The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
-
B.
HOMFLY-PT polynomial
The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
-
C.
Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
-
D.
topological quantum field theory
A topological quantum field theory is a quantum field theory whose observables and correlation functions depend only on the topology of the underlying spacetime manifold rather than its geometric details, making it a powerful tool in both mathematics and theoretical physics.
-
E.
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.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
3-manifold invariant
ⓘ
link invariant ⓘ quantum invariant ⓘ quantum topology object ⓘ topological invariant ⓘ |
| appliesTo |
closed 3-manifolds
ⓘ
framed links ⓘ links in 3-manifolds ⓘ oriented 3-manifolds ⓘ |
| associatedWith |
mapping class group representations
ⓘ
modular functors ⓘ |
| constructedBy |
Nicolai Reshetikhin
NERFINISHED
ⓘ
Vladimir Turaev NERFINISHED ⓘ |
| dependsOn |
choice of root of unity
ⓘ
quantum group at a root of unity ⓘ |
| derivedFrom |
Chern–Simons theory
NERFINISHED
ⓘ
quantum groups ⓘ |
| field |
geometric topology
ⓘ
low-dimensional topology ⓘ mathematical physics ⓘ quantum topology ⓘ |
| inspiredBy | Witten’s Chern–Simons path integral NERFINISHED ⓘ |
| invariantUnder |
Kirby moves
NERFINISHED
ⓘ
orientation-preserving homeomorphisms of 3-manifolds ⓘ |
| namedAfter |
Edward Witten
NERFINISHED
ⓘ
Nicolai Reshetikhin NERFINISHED ⓘ Vladimir Turaev NERFINISHED ⓘ |
| parameterizedBy |
compact Lie group
ⓘ
level k ⓘ |
| realizes | 3-dimensional topological quantum field theory ⓘ |
| relatedTo |
Chern–Simons partition function
NERFINISHED
ⓘ
HOMFLY-PT polynomial NERFINISHED ⓘ Jones polynomial NERFINISHED ⓘ Reshetikhin–Turaev TQFT NERFINISHED ⓘ Turaev–Viro invariant NERFINISHED ⓘ topological quantum field theory ⓘ |
| satisfies |
Kirby calculus invariance
ⓘ
surgery formula ⓘ |
| specialCase |
SU(2) quantum invariants
ⓘ
SU(N) quantum invariants ⓘ |
| usedFor |
constructing 3D TQFTs
ⓘ
distinguishing 3-manifolds ⓘ studying knot and link complements ⓘ |
| uses |
modular tensor categories
ⓘ
quantum group representations ⓘ ribbon categories ⓘ |
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: Witten–Reshetikhin–Turaev invariant Description of subject: The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Witten–Reshetikhin–Turaev invariants
this entity surface form:
Reshetikhin–Turaev invariants