2-knots with solvable group

Details 2-knots with solvable group 2-knots with solvable group

2010-03-29

arxiv.org/abs/1003.5408v1

Journal of Knot Theory and Its Ramifications 20 (2011), 977--994

Mathematics

Geometric Topology

Scientific paper

10.1142/S021821651100898X

We complete the TOP classification of 2-knots with torsion-free, solvable knot group by showing that fibred 2-knots with closed fibre the Hantzsche-Wendt flat 3-manifold $HW$ are not reflexive, while every fibred 2-knot with closed fibre a $\mathbb{N}il^3$-manifold with base orbifold $S^2(3,3,3)$ is reflexive, and by giving explicit normal forms for the strict weight orbits of normal generators for the groups of all knots in either class. We also determine when the knots are amphicheiral or invertible, and show that the only non-trivial doubly null-concordant knots with such groups are those with group $\pi\tau_29_{46}$.

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