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.

© 1996-9

1999-05-24