Fundamental theorems in global knot theory. I
This is an announcement of results on smooth codimension two knotted spheres in closed manifolds M. 1) Seifert surfaces exist, when homologically possible, and have connectivity as high as allowed by the homotopy of the complement of the knot in M. 2) Fibred knots exist in highly connected M - in particular in \(S^ n\times S^{n+1}\). This latter example is null-homotopic but not local, i.e. contained in a ball. 3) Criteria are given in terms of the homology of the infinite cyclic covering of the complement, when M is highly connected, for certain classes of knots to be local or to be unknotted. \(\{\) For part II, see the following review.\(\}\).
smooth codimension two knotted spheres in closed manifolds
infinite cyclic covering of the complement
scientific article; zbMATH DE number 3909354