annulus conjecture

annulus conjecture [′an·yə·ləs kən′jek·chər]

(mathematics)

For dimensionn,the assertion that iffandgare locally flat embeddings of the (n- 1) sphere,S^{n- 1}, in realnspace,Rⁿ, withf(S^{n- 1}) in the bounded component ofRⁿ-g(S^{n- 1}), then the closed region inRⁿbounded byf(S^{n- 1}) andg(S^{n- 1}) is homeomorphic to the direct product ofS^{n- 1}and the closed interval [0,1]; it is established forn≠ 4.