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- In mathematics, a tangle is generally one of two related concepts:
* In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary.
* In link theory, a tangle is an embedding of n arcs and m circles into – the difference from the previous definition is that it includes circles as well as arcs, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance. (A quite different use of 'tangle' appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, Journal of Combinatorial Theory B 52 (1991) 153–190, who used it to describe separation in graphs. This usage has been extended to matroids.) The balance of this article discusses Conway's sense of tangles; for the link theory sense, see that article. Two n-tangles are considered equivalent if there is an ambient isotopy of one tangle to the other keeping the boundary of the 3-ball fixed. Tangle theory can be considered analogous to knot theory except instead of closed loops we use strings whose ends are nailed down. See also braid theory. (en)
- 数学の分野において、タングル (tangle) は結び目の一部分を切り取って得られるような幾何的対象のことである。通常次の二種類のいずれかを指す。
* ある 2次元球面で切り取って得られるもの。以下のタングル(1)。
* 平行な二つの平面で切り取って得られるもの。以下のタングル(2)。 これらは共に「境界付き 3次元多様体に埋め込まれた、 1次元の(境界付き)多様体」とみなせるが、これら二種類のタングル(もしくはその一般化)が統一的に扱われることはないようである。 (ja)
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- 7767 (xsd:nonNegativeInteger)
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- 数学の分野において、タングル (tangle) は結び目の一部分を切り取って得られるような幾何的対象のことである。通常次の二種類のいずれかを指す。
* ある 2次元球面で切り取って得られるもの。以下のタングル(1)。
* 平行な二つの平面で切り取って得られるもの。以下のタングル(2)。 これらは共に「境界付き 3次元多様体に埋め込まれた、 1次元の(境界付き)多様体」とみなせるが、これら二種類のタングル(もしくはその一般化)が統一的に扱われることはないようである。 (ja)
- In mathematics, a tangle is generally one of two related concepts:
* In John Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n marked points on the ball's boundary.
* In link theory, a tangle is an embedding of n arcs and m circles into – the difference from the previous definition is that it includes circles as well as arcs, and partitions the boundary into two (isomorphic) pieces, which is algebraically more convenient – it allows one to add tangles by stacking them, for instance. (en)
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- タングル (ja)
- Tangle (mathematics) (en)
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