Wild knot (nonfiction): Difference between revisions
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In the mathematical theory of knots, a wild knot is a knot that is not tame. Wild knots can have pathological behavior. | [[File:Wild knot.png|thumb|A wild knot.]]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 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. | ||
Revision as of 17:51, 26 June 2017
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.
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Fiction cross-reference
Nonfiction cross-reference
External links:
- Wild knot @ Wikipedia