Let be the knot above, and let the homomorphism taking a knot to its companion knot be faithful (i.e., taking the preferred longitude and meridian of the original torus to the referred longitude and latitude of the tubular neighborhood). Then is an untwisted doubled knot of . Otherwise, is a doubled knot with twists (Rolfsen 1976, p. 112).
Doubled Knot
See also
Cable Knot, Companion Knot, Satellite Knot, Twist Knot, Whitehead DoubleExplore with Wolfram|Alpha
References
Livingston, C. Knot Theory. Washington, DC: Math. Assoc. Amer., pp. 35, 73, 146, and 154-155, 1993.Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 112, 166-167, and 225, 1976.Whitehead, J. H. C. "On Doubled Knots." J. London Math. Soc. 12, 63-71, 1937.Referenced on Wolfram|Alpha
Doubled KnotCite this as:
Weisstein, Eric W. "Doubled Knot." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DoubledKnot.html