Doubled Knot


Let K be the knot above, and let the homomorphism h taking a knot K_1 to its companion knot K_2 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 K_2 is an untwisted doubled knot of K_1. Otherwise, K_2 is a doubled knot with q twists (Rolfsen 1976, p. 112).

See also

Cable Knot, Companion Knot, Satellite Knot, Twist Knot, Whitehead Double

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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.

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Doubled Knot

Cite this as:

Weisstein, Eric W. "Doubled Knot." From MathWorld--A Wolfram Web Resource.

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