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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On metabelian two-knot groups


Author: Jonathan A. Hillman
Journal: Proc. Amer. Math. Soc. 96 (1986), 372-374
MSC: Primary 57Q45
DOI: https://doi.org/10.1090/S0002-9939-1986-0818474-3
MathSciNet review: 818474
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818474-3
Keywords: Commutator subgroup, injectivity of cup product, metabelian, Milnor duality, two-knot
Article copyright: © Copyright 1986 American Mathematical Society