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.
- 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, doi:10.2140/gt.2010.14.2305, MR 2740649.
- 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.
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