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Slice Knot

A Knot $K$ in $\Bbb{S}^3=\partial\Bbb{D}^4$ is a slice knot if it bounds a Disk $\Delta^2$ in $\Bbb{D}^4$ which has a Tubular Neighborhood $\Delta^2\times\Bbb{D}^2$ whose intersection with $\Bbb{S}^3$ is a Tubular Neighborhood $K\times\Bbb{D}^2$ for $K$.

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

See also Ribbon Knot, Tubular Neighborhood


Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 218, 1976.

© 1996-9 Eric W. Weisstein