Let and be disjoint bicollared knots in or and let denote the open region between them. Then the closure of is a closed annulus . Except for the case , 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.