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.
Observed surface forms (3)
| Surface form | Occurrences |
|---|---|
| Reidemeister move I | 0 |
| Reidemeister move II | 0 |
| Reidemeister move III | 0 |
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
NERFINISHED
ⓘ
Reidemeister move II NERFINISHED ⓘ Reidemeister move III NERFINISHED ⓘ |
| 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 NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.