Kauffman polynomial

E656684

knot invariant link invariant

The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.

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Observed surface forms (1)

Surface form	Occurrences
Kauffman bracket	1

Statements (38)

Predicate	Object
instanceOf	knot invariant ⓘ link invariant ⓘ
appliesTo	oriented links ⓘ unoriented links ⓘ
associatedWith	knot diagrams ⓘ
canBeSpecializedTo	Jones polynomial NERFINISHED ⓘ
captures	topological information about knots ⓘ topological information about links ⓘ
codomain	Laurent polynomials in two variables ⓘ
definedFor	knots ⓘ links ⓘ
definedUsing	skein relation ⓘ state sum model ⓘ
dependsOn	two variables ⓘ
domain	isotopy classes of links in 3-space ⓘ
extends	Jones polynomial NERFINISHED ⓘ
field	knot theory ⓘ low-dimensional topology ⓘ
generalizes	Jones polynomial NERFINISHED ⓘ
hasApplication	classification of knots and links ⓘ construction of quantum invariants ⓘ
hasProperty	regular isotopy invariant ⓘ
hasType	two-variable polynomial ⓘ
introducedBy	Louis H. Kauffman NERFINISHED ⓘ
is	a refinement of information given by the Jones polynomial ⓘ
isInvariantUnder	Reidemeister moves NERFINISHED ⓘ ambient isotopy ⓘ
namedAfter	Louis H. Kauffman NERFINISHED ⓘ
relatedConcept	framed links ⓘ regular isotopy ⓘ
relatedTo	HOMFLY-PT polynomial NERFINISHED ⓘ Jones polynomial NERFINISHED ⓘ
satisfies	skein relations distinct from Jones polynomial ⓘ
studiedIn	quantum topology ⓘ
usedIn	distinguishing non-equivalent knots ⓘ study of link diagrams ⓘ
usedToDefine	certain quantum link invariants ⓘ
variableCount	two ⓘ

Referenced by (2)

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

Jones polynomial → relatedTo → Kauffman polynomial ⓘ

Jones polynomial → canBeComputedUsing → Kauffman polynomial ⓘ

this entity surface form: Kauffman bracket