Seifert fibred knot manifolds

J.A.Hillman

Abstract

We consider the question of when is the closed manifold obtained by elementary surgery on an \(n\)-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases \(n=2\) and 3. We have found a new family of 2-knots with torsion-free, solvable group, overlooked in earlier work. We show also that there are no aspherical Seifert fibred 3-knot manifolds. We know of no higher dimensional examples.

Keywords: knot, Seifert fibred, \(0\)-framed surgery.

AMS Subject Classification: Primary 57M25; secondary 57Q45.