Let 
and 
be disjoint bicollared knots in 
or 
and let 
denote the open region between them. Then the closure of 
is a closed annulus ![S^n×[0,1]](/images/equations/AnnulusTheorem/Inline7.svg)
. Except for the case 
, the theorem was proved by Kirby (1969).
Annulus Theorem
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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.Referenced on Wolfram|Alpha
Annulus TheoremCite this as:
Weisstein, Eric W. "Annulus Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AnnulusTheorem.html