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Satellite knot

Index Satellite knot

In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement. [1]

14 relations: Borromean rings, Boundary parallel, Geometrization conjecture, Horst Schubert, Hyperbolic link, Incompressible surface, JSJ decomposition, Knot (mathematics), Knot complement, Knot theory, Prime knot, Torus, Torus knot, Whitehead link.

Borromean rings

In mathematics, the Borromean rings consist of three topological circles which are linked and form a Brunnian link (i.e., removing any ring results in two unlinked rings).

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Boundary parallel

In mathematics, a closed n-manifold N embedded in an (n + 1)-manifold M is boundary parallel (or ∂-parallel, or peripheral) if there is an isotopy of N onto a boundary component of M.

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Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that certain three-dimensional topological spaces each have a unique geometric structure that can be associated with them.

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Horst Schubert

Horst Schubert (11 June 1919 – 2001) was a German mathematician.

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Hyperbolic link

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry.

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Incompressible surface

In mathematics, an incompressible surface, in intuitive terms, is a surface, embedded in a 3-manifold, which has been simplified as much as possible while remaining "nontrivial" inside the 3-manifold.

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JSJ decomposition

In mathematics, the JSJ decomposition, also known as the toral decomposition, is a topological construct given by the following theorem: The acronym JSJ is for William Jaco, Peter Shalen, and Klaus Johannson.

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Knot (mathematics)

In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

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Knot complement

In mathematics, the knot complement of a tame knot K is the three-dimensional space surrounding the knot.

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Knot theory

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

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Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.

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In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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Torus knot

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3.

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Whitehead link

In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links.

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Redirects here:

Cable knot, Satellite link (knot theory), Swallow-follow torus, Whitehead double.


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

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