Wild knot (nonfiction): Difference between revisions
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Latest revision as of 14:39, 22 November 2021
In the mathematical theory of knots, a wild knot is a knot that is not tame. Wild knots can have pathological behavior.
A knot is tame if it can be "thickened up" -- that is, if there exists an extension to an embedding of the solid torus S 1 × D 2 into the 3-sphere.
A knot is tame if and only if it can be represented as a finite closed polygonal chain.
Smooth knots, for example, are always tame.
In knot theory and 3-manifold theory, often the adjective "tame" is omitted.
Wild knots can be found in some Celtic designs.