On Metabelian Two-Knot Groups

Jonathan A. Hillman

Type: Article

Publication Date: 1986-02-01

Citations: 0

DOI: https://doi.org/10.2307/2046183

Abstract

We show that if the commutator subgroup of a $2$-knot group is abelian but not finitely generated, then it is isomorphic to the additive group of dyadic rationals, thus eliminating the one possibility left open in recent work of Yoshikawa. It follows that the examples given by Cappell and Fox provide a complete list of metabelian $2$-knot groups.

Locations

Proceedings of the American Mathematical Society - View - PDF

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Works Cited by This (4)

Action	Title	Year	Authors
+	DUALITY IN AN INFINITE CYCLIC COVERING AND EVEN-DIMENSIONAL KNOTS	1977	Michael Färber
+	On the intersection ring of compact three manifolds	1975	Dennis Sullivan
+ PDF Chat	High dimensional knot groups which are not two-knot groups	1977	Jonathan A. Hillman
+	On 2-Knot Groups with Abelian Commutator Subgroups	1984	Katsuyuki Yoshikawa