Conway skein triple (L₊, L₋, L₀)
E169188
The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway skein triple (L₊, L₋, L₀) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1483891 — 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: Conway skein triple (L₊, L₋, L₀) Context triple: [Conway polynomial, definedBy, Conway skein triple (L₊, L₋, L₀)]
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
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C.
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.
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D.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
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E.
triskelion
A triskelion is an ancient symbol consisting of three interlocked spirals or bent human legs radiating from a central point, commonly associated with Celtic and Mediterranean cultures.
- 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: Conway skein triple (L₊, L₋, L₀) Target entity description: The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
-
A.
Conway notation for knots
Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
-
B.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
-
C.
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.
-
D.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
E.
triskelion
A triskelion is an ancient symbol consisting of three interlocked spirals or bent human legs radiating from a central point, commonly associated with Celtic and Mediterranean cultures.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
configuration of link diagrams
ⓘ
link diagram ⓘ link diagram ⓘ link diagram ⓘ skein triple ⓘ |
| appearsIn |
literature on polynomial link invariants
ⓘ
literature on skein modules ⓘ |
| appliesTo | oriented link diagrams ⓘ |
| associatedWith |
Conway polynomial
ⓘ
surface form:
Alexander–Conway polynomial
Conway polynomial ⓘ skein relation ∇(L₊) − ∇(L₋) = z ∇(L₀) ⓘ |
| constraint |
L₀ is obtained from L₊ and L₋ by smoothing that crossing
ⓘ
L₊ and L₋ differ only by the sign of one crossing ⓘ |
| definedBy | local modification at a single crossing ⓘ |
| domain | oriented links in S³ ⓘ |
| field | knot theory ⓘ |
| generalizationOf | skein triples for other link polynomials ⓘ |
| hasPart |
L₀
ⓘ
L₊ ⓘ L₋ ⓘ |
| hasProperty |
contains a specified negative crossing
ⓘ
contains a specified positive crossing ⓘ obtained by smoothing the specified crossing ⓘ |
| introducedInContextOf | John Horton Conway’s work on knot polynomials ⓘ |
| locality | diagrams coincide outside a small disk containing the crossing ⓘ |
| mathematicalDiscipline | low-dimensional topology ⓘ |
| notationUsedIn | standard textbooks on knot theory ⓘ |
| relatedTo |
Alexander polynomial
ⓘ
HOMFLY-PT polynomial ⓘ Jones polynomial ⓘ |
| requires | choice of a distinguished crossing in L₊ and L₋ ⓘ |
| usedFor |
defining skein relations
ⓘ
defining the Conway polynomial ⓘ expressing changes of link invariants under local crossing modifications ⓘ studying link invariants ⓘ |
| usedIn |
inductive proofs of properties of link invariants
ⓘ
recursive computation of the Conway polynomial ⓘ |
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: Conway skein triple (L₊, L₋, L₀) Description of subject: The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.