Kauffman polynomial
E656684
The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Kauffman bracket | 1 |
| Kauffman polynomial canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338448 — 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: Kauffman polynomial Context triple: [Jones polynomial, relatedTo, Kauffman polynomial]
-
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.
Witten–Reshetikhin–Turaev 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.
-
D.
Conway polynomial
The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
-
E.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
- 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: Kauffman polynomial Target entity description: The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
-
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.
Witten–Reshetikhin–Turaev 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.
-
D.
Conway polynomial
The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
-
E.
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
- F. None of above. chosen
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 ⓘ |
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: Kauffman polynomial Description of subject: The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Kauffman bracket