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About: Wild knot     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatKnotsAndLinks, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:Abstraction100002137yago:Agglomeration107959269yago:Bunch107959943yago:Collection107951464yago:Group100031264yago:Knot107960384yago:WikicatKnotsAndLinks New Facet based on Instances of this Class

In the mathematical theory of knots, a knot is tame if it can be "thickened up", that is, if there exists an extension to an embedding of the solid torus into the 3-sphere. A knot is tame if and only if it can be represented as a finite closed polygonal chain. Every closed curve containing a wild arc is a wild knot. Knots that are not tame are called wild and can have pathological behavior. In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame. It has been conjectured that every has infinitely many quadrisecants.