Annulus Theorem

Let $K_1^n$ and $K_2^n$ be disjoint bicollared knots in $\Bbb{R}^{n+1}$ or $\Bbb{S}^{n+1}$ and let $U$ denote the open region between them. Then the closure of $U$ is a closed annulus $\Bbb{S}^n\times [0,1]$. Except for the case $n=3$, the theorem was proved by Kirby (1969).

References

Kirby, R. C. ``Stable Homeomorphisms and the Annulus Conjecture.'' Ann. Math. 89, 575-582, 1969.

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 38, 1976.