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 ${\displaystyle K\subset S^{3}}$ is slice if it bounds a nicely embedded disk D in the 4-ball.

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 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.

The signature of a slice knot is zero.

The Alexander polynomial of a slice knot factors as a product ${\displaystyle f(t)f(t^{-1})}$ where ${\displaystyle f(t)}$ is some integral Laurent polynomial. This is known as the Fox–Milnor condition.

...
Wikipedia