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A slice knot is a type of mathematical knot. It helps to remember that 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. 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. Any 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 f(t)f(t − 1) where f(t) is some integral Laurent polynomial. This is known as the Fox-Milnor condition. The following is a list of all slice knots with 10 or fewer crossings; it was compiled using the Knot Atlas: 61, 88, 89, 820, 927, 941, 946, 103, 1022, 1035, 1042, 1048, 1075, 1087, 1099, 10123, 10129, 10137, 10140, 10153 and 10155. This topology-related article is a stub. You can help Wikipedia by expanding it. v • d • e