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.
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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
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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
Lead section
Kurt Reidemeister (1927) and, independently, James Waddell Alexander and Garland Baird Briggs (1926), demonstrated that two knot diagrams belonging to the same knot, up to planar isotopy, can be related by a sequence of the three Reidemeister moves.
In Group: Geometric and Differential Topology, Article text
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram.
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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