Slice knot
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 B4, then K is said to be smoothly slice. If K 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]: 61, , , , , , , , , , , , , , , , , , , and .
References
See also
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