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Ribbon Knot

If the Knot $K$ is the boundary $K=f(\Bbb{S}^1)$ of a singular disk $f:\Bbb{D}\to\Bbb{S}^3$ which has the property that each self-intersecting component is an arc $A\subset f(\Bbb{D}^2)$ for which $f^{-1}(A)$ consists of two arcs in $\Bbb{D}^2$, 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.

See also Slice Knot


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

© 1996-9 Eric W. Weisstein