Reidemeister moves
E656683
Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Reidemeister moves canonical | 7 |
| Reidemeister move I | 1 |
| Reidemeister move II | 1 |
| Reidemeister move III | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7338443 — 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: Reidemeister moves Context triple: [Jones polynomial, invariantUnder, Reidemeister moves]
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A.
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.
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B.
Dehn twist
A Dehn twist is a fundamental type of self-homeomorphism of a surface obtained by cutting along a simple closed curve, twisting one side by 360 degrees, and gluing it back, playing a central role in low-dimensional topology and the study of mapping class groups.
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C.
Conway skein triple (L₊, L₋, L₀)
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.
-
D.
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.
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E.
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.
- 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: Reidemeister moves Target entity description: Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
-
A.
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.
-
B.
Dehn twist
A Dehn twist is a fundamental type of self-homeomorphism of a surface obtained by cutting along a simple closed curve, twisting one side by 360 degrees, and gluing it back, playing a central role in low-dimensional topology and the study of mapping class groups.
-
C.
Conway skein triple (L₊, L₋, L₀)
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
Reidemeister move
ⓘ
concept in knot theory ⓘ local diagrammatic transformations ⓘ |
| alsoKnownAs |
poke move
ⓘ
slide move ⓘ twist move ⓘ |
| appliesTo |
knot diagrams
ⓘ
link diagrams ⓘ |
| characterizes |
ambient isotopy of knots
ⓘ
equivalence of knot diagrams ⓘ |
| definedOn |
oriented knot diagrams
ⓘ
unoriented knot diagrams ⓘ |
| description |
adds or removes a pair of crossings
ⓘ
adds or removes a single twist in a strand ⓘ slides one strand over a crossing of two others ⓘ |
| field |
knot theory
ⓘ
topology ⓘ |
| formalizedAs | moves on planar knot diagrams ⓘ |
| generalizationOf | local moves in link diagrams ⓘ |
| hasPart |
Reidemeister move I
ⓘ
linked to:
Reidemeister moves
Reidemeister move II ⓘ
linked to:
Reidemeister moves
Reidemeister move III ⓘ
linked to:
Reidemeister moves
|
| hasProperty |
complete for knot diagram equivalence
ⓘ
finite generating set of local moves ⓘ invertible moves ⓘ local transformations ⓘ |
| implies | same topological knot type ⓘ |
| influenced | diagrammatic approaches in low-dimensional topology ⓘ |
| namedAfter | Kurt Reidemeister ⓘ |
| partOf | classical knot theory ⓘ |
| relatedTo |
ambient isotopy
ⓘ
knot invariants ⓘ link invariants ⓘ planar projections of knots ⓘ |
| requires | preservation of diagram outside a small disk ⓘ |
| statedIn | Kurt Reidemeister’s work on knot theory ⓘ |
| usedFor |
deciding when two diagrams represent the same knot
ⓘ
proving knot invariance ⓘ simplifying knot diagrams ⓘ |
| usedIn |
algorithmic knot recognition
ⓘ
combinatorial knot theory ⓘ proofs of invariance of the Alexander polynomial ⓘ proofs of invariance of the Jones polynomial ⓘ |
| yearProposed | 1926 ⓘ |
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: Reidemeister moves Description of subject: Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
Referenced by (10)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Reidemeister moves
linked to: Reidemeister moves
linked to: Reidemeister moves