Ribbon Knot

If the knot K is the boundary K=f(S^1) of a singular disk f:D->S^3 which has the property that each self-intersecting component is an arc A subset f(D^2) for which f^(-1)(A) consists of two arcs in D^2, one of which is interior, then K is said to be a ribbon knot.

Every ribbon knot is a slice knot, and it is conjectured that every slice knot is a ribbon knot.

Knot 9_(46), illustrated above, is a ribbon knot (Rolfsen 1976, p. 225).

See also

Slice Knot

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Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 225, 1976.

Referenced on Wolfram|Alpha

Ribbon Knot

Cite this as:

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

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