Annulus Theorem

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

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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.

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