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2-KNOTS WITH SOLVABLE GROUPS

JONATHAN A. HILLMAN

School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia

https://doi.org/10.1142/S021821651100898XCited by:2 (Source: Crossref)

Abstract

We show that fibered 2-knots with closed fiber the Hantzsche–Wendt flat 3-manifold are not reflexive, while every fibered 2-knot with closed fiber a Nil-manifold with base orbifold S(3, 3, 3) is reflexive. We also determine when the knots are amphicheiral or invertible, and give explicit representatives for the possible meridians (up to automorphisms of the knot group which induce the identity on abelianization) for the groups of all knots in either class. This completes the TOP classification of 2-knots with torsion-free, elementary amenable knot group. In the final section, we show that the only non-trivial doubly null-concordant knots with such groups are those with the group of the 2-twist spin of the knot 9₄₆.

Keywords:

AMSC: 57Q45

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