High Quality Content by WIKIPEDIA articles! In the mathematical theory of knots, a satellite knot is a knot which contains an incompressible, non-boundary parallel torus in its complement. The class of satellite knots include composite knots, cable knots and Whitehead doubles.A satellite knot K can be picturesquely described as follows: start by taking a nontrivial knot K' lying inside an unknotted solid torus V. Here "nontrivial" means that the knot K' is not allowed to sit inside of a 3-ball in V and K' is not allowed to be isotopic to the central core curve of the solid torus. Then tie up the solid torus into a nontrivial knot.

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