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).

# 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.

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Annulus Theorem## Cite this as:

Weisstein, Eric W. "Annulus Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AnnulusTheorem.html