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 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. 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. 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 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. 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.