A **slice knot** is a type of mathematical knot. In knot theory, a "knot" means an embedded circle in the 3-sphere

and that the 3-sphere can be thought of as the boundary of the four-dimensional ball

A knot is **slice** if it bounds a nicely embedded disk *D* in the 4-ball.^{[1]}

What is meant by "nicely embedded" depends on the context, and there are different terms for different kinds of slice knots. If *D* is smoothly embedded in *B ^{4}*, then

*K*is said to be

**smoothly slice**. If

*D*is only locally flat (which is weaker), then

*K*is said to be

**topologically slice**.

Every ribbon knot is smoothly slice. An old question of Fox asks whether every slice knot is actually a ribbon knot.^{[2]}

The signature of a slice knot is zero.^{[3]}

The Alexander polynomial of a slice knot factors as a product where is some integral Laurent polynomial.^{[3]} This is known as the **Fox–Milnor condition**.^{[4]}

The following is a list of all slice knots with 10 or fewer crossings; it was compiled using the Knot Atlas^{[full citation needed]}: 6_{1},^{[5]} , , , , , , , , , , , , , , , , , , and .

## See also

## References

**^**Lickorish, W. B. Raymond (1997),*An Introduction to Knot Theory*, Graduate Texts in Mathematics,**175**, Springer, p. 86, ISBN 9780387982540.**^**Gompf, Robert E.; Scharlemann, Martin; Thompson, Abigail (2010), "Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures",*Geometry & Topology*,**14**(4): 2305–2347, arXiv:1103.1601 , doi:10.2140/gt.2010.14.2305, MR 2740649.- ^
^{a}^{b}Lickorish (1997), p. 90. **^**Banagl, Markus; Vogel, Denis (2010),*The Mathematics of Knots: Theory and Application*, Contributions in Mathematical and Computational Sciences,**1**, Springer, p. 61, ISBN 9783642156373.**^**"6 1",*The Knot Atlas*.