2-Knots with solvable groups

Jonathan A. Hillman

Abstract

The 2-knots with torsion-free, elementary amenable knot group and which have not yet been fully classified are fibred, with closed fibre the Hantzsche-Wendt flat 3-manifold HW or a Nil-manifold with base orbifold S(3,3,3). We give explicit normal forms for the strict weight orbits of normal generators for the groups of such knots, and determine when the knots are amphicheiral or invertible.

Keywords: amphicheiral. flat. Hantzsche-Wendt. invertible. 2-knot. Nil-manifold. reflexive. strict weight orbit.

AMS Subject Classification: Primary 57Q45.