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If you have an embedding of a 1-Sphere in a 3-Manifold which exists continuously over the 2-Disk, then it also extends over the Disk as an embedding. It was proposed by Dehn in 1910, but a correct proof was not obtained until the work of Papakyriakopoulos (1957ab).
References
Hempel, J. 3-Manifolds. Princeton, NJ: Princeton University Press, 1976.
Papakyriakopoulos, C. D. ``On Dehn's Lemma and the Asphericity of Knots.'' Proc. Nat. Acad. Sci. USA
43, 169-172, 1957a.
Papakyriakopoulos, C. D. ``On Dehn's Lemma and the Asphericity of Knots.'' Ann. Math. 66, 1-26, 1957b.
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, pp. 100-101, 1976.