A loop theorem for duality spaces and fibred ribbon knots
In this paper it is proved that a fibered knot in a homology 3-sphere is homotopically ribbon if and only if its (closed) monodromy extends over a handlebody. The proof of this result is based on an extension of the loop theorem as established by the authors. The authors show how their characterization of homotopically ribbon knots can be utilized to construct explicit examples of knots in the boundary of a contractible 4- manifold V, which either do not bound PL-discs in V, or which are slice but not homotopically ribbon. Finally, a question of Scharlemann concerning concordances of torus knots is answered affirmatively for the larger class of \({\mathbb{Q}}\)-anisotropic [the second author, Math. Ann. 257, 157-170 (1981; Zbl 0451.57001)] fibered knots in homology 3-spheres.
loop theorem in 3-dimensional Poincaré duality spaces
scientific article; zbMATH DE number 3856013
scientific article