Reidemeister's Theorem states that two diagrams of a knot or link represent the same knot or link up to ambient isotopy if and only if one diagram can be transformed into the other by a finite sequence of three local moves, now called the Reidemeister moves. Named for Kurt Reidemeister, it is the foundational combinatorial result of knot theory, reducing questions about continuous deformation of knots in three-dimensional space to purely diagrammatic, finite calculations.
Facts
StatementTwo knot diagrams belonging to the same knot, up to planar isotopy, can be related by a sequence of the three Reidemeister moves. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Reidemeister move (Wikipedia)
Sources
1. Reidemeister move (Wikipedia)
Lead section
two knot diagrams belonging to the same knot, up to planar isotopy, can be related by a sequence of the three Reidemeister moves
History section
The theorem was demonstrated by Kurt Reidemeister in 1927, and independently by James Waddell Alexander and Garland Baird Briggs in 1926.
In Branch: Knot Theory, Lead sentence
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram.
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