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Date: 8-8-2021
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Let be a knot that is geometrically essential in a standard embedding of the solid torus in the three-sphere . Let be another knot and let be a tubular neighborhood of in . Finally, let be a homeomorphism and let . Then is a companion knot of the knot (Rolfsen 1976, p. 111) and is called the satellite knot of (Adams 1994, pp. 115-118).
REFERENCES:
Adams, C. C. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 115-118, 1994.
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 225, 1976.
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مدرسة دار العلم.. صرح علميّ متميز في كربلاء لنشر علوم أهل البيت (عليهم السلام)
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