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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.
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.
The signature of a slice knot is zero.
The Alexander polynomial of a slice knot factors as a product where is some integral Laurent polynomial. This is known as the Fox–Milnor condition.
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