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Wild knot

Index 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. [1]

7 relations: Knot theory, Pathological (mathematics), Polygonal chain, Solid torus, Wild arc, 3-manifold, 3-sphere.

Knot theory

In topology, knot theory is the study of mathematical knots.

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Pathological (mathematics)

In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved.

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Polygonal chain

In geometry, a polygonal chain is a connected series of line segments.

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Solid torus

In mathematics, a solid torus is the topological space formed by sweeping a disk around a circle.

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Wild arc

In geometric topology, a wild arc is an embedding of the unit interval into 3-dimensional space not equivalent to the usual one in the sense that there does not exist an ambient isotopy taking the arc to a straight line segment.

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3-manifold

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space.

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3-sphere

In mathematics, a 3-sphere, or glome, is a higher-dimensional analogue of a sphere.

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Redirects here:

Framing (knot), Tame knot, Wild link.

References

[1] https://en.wikipedia.org/wiki/Wild_knot

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