Wild knot

A wild knot.

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 S¹ × D² into the 3-sphere. A knot is tame if and only if it can be represented as a finite closed polygonal chain. 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. Wild knots can be found in some Celtic designs.

References

Knot theory (knots and links)

Hyperbolic	Figure-eight (4₁) Three-twist (5₂) Stevedore (6₁) 6₂ 6₃ Endless (7₄) Carrick mat (8₁₈) Perko pair (10₁₆₁) (−2,3,7) pretzel (12n242) Whitehead (52 1) Borromean rings (63 2) L10a140

Satellite	Composite knots Granny Square Knot sum

Torus	Unknot (0₁) Trefoil (3₁) Cinquefoil (5₁) Septafoil (7₁) Unlink (02 1) Hopf (22 1) Solomon's (42 1)

Invariants	Alternating Arf invariant Bridge no. 2-bridge Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking no. Polynomial Alexander Bracket HOMFLY Jones Kauffman Pretzel Prime list Stick no. Tricolorability Unknotting no. & problem

Notation & operations	Alexander–Briggs notation Conway notation Dowker notation Flype Mutation Reidemeister move Skein relation Tabulation

Other	Alexander's theorem Berge Braid theory Conway sphere Complement Double torus Fibered Knot List of knots and links Ribbon Slice Sum Tait conjectures Twist Wild Writhe

Category Commons

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Wild knot

See also

References