annulus conjecture

annulus conjecture

[′an·yə·ləs kən′jek·chər]
(mathematics)
For dimension n, the assertion that if f and g are locally flat embeddings of the (n- 1) sphere, S n- 1, in real n space, Rn, with f (S n- 1) in the bounded component of Rn-g (S n- 1), then the closed region in Rn bounded by f (S n- 1) and g (S n- 1) is homeomorphic to the direct product of S n- 1and the closed interval [0,1]; it is established for n ≠ 4.