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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Observed surface forms (2)

Surface form	Occurrences
Reshetikhin–Turaev invariants	1
Witten–Reshetikhin–Turaev invariants	1

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 ⓘ

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 invariant ⓘ

this entity surface form: Witten–Reshetikhin–Turaev invariants

Chern–Simons theory → relatedTo → Witten–Reshetikhin–Turaev invariant ⓘ

this entity surface form: Reshetikhin–Turaev invariants