Witten–Reshetikhin–Turaev invariant

E508543

3-manifold invariant link invariant quantum invariant quantum topology object topological invariant

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.

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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 ⓘ Vladimir Turaev ⓘ
dependsOn	choice of root of unity ⓘ quantum group at a root of unity ⓘ
derivedFrom	Chern–Simons theory ⓘ quantum groups ⓘ
field	geometric topology ⓘ low-dimensional topology ⓘ mathematical physics ⓘ quantum topology ⓘ
inspiredBy	Witten’s Chern–Simons path integral ⓘ linked to: Chern–Simons theory
invariantUnder	Kirby moves ⓘ orientation-preserving homeomorphisms of 3-manifolds ⓘ
namedAfter	Edward Witten ⓘ Nicolai Reshetikhin ⓘ Vladimir Turaev ⓘ
parameterizedBy	compact Lie group ⓘ level k ⓘ
realizes	3-dimensional topological quantum field theory ⓘ
relatedTo	Chern–Simons partition function ⓘ linked to: Chern–Simons theory HOMFLY-PT polynomial ⓘ Jones polynomial ⓘ Reshetikhin–Turaev TQFT ⓘ linked to: topological quantum field theory Turaev–Viro invariant ⓘ 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

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

topological quantum field theory → producesInvariant → Witten–Reshetikhin–Turaev invariant ⓘ

Jones polynomial → connectedTo → Witten–Reshetikhin–Turaev invariants ⓘ

linked to: Witten–Reshetikhin–Turaev invariant

Chern–Simons theory → relatedTo → Reshetikhin–Turaev invariants ⓘ