Small knots in Seifert fibered 3-manifolds
Constructing knots with given properties in arbitrary 3-manifolds turns out to be a rather difficult problem. The question we consider here is: at which conditions does an arbitrary 3-manifold contain a small knot, i.e. a knot without closed incompressible surfaces in its exterior excepted peripheral tori? Actually one can hope that such knots exist at least in non-Haken 3-manifolds; this may be interesting in this case since such knots have a property which is very close to the one possessed by the ambient manifold. In this paper we prove that non-trivial small knots exist in non-Haken Seifert fibered 3-manifolds (by non-trivial knots we mean knots that are not fibers of the Seifert fibration).
knot without closed incompressible surfaces in its exterior
scientific article; zbMATH DE number 549741