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Proceedings of the American Mathematical Society

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



Longitudes of a link and principality of an Alexander ideal

Author: Jonathan A. Hillman
Journal: Proc. Amer. Math. Soc. 72 (1978), 370-374
MSC: Primary 57M25
MathSciNet review: 507341
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Abstract: In this note it is shown that the longitudes of a $ \mu $-component homology boundary link L are in the second commutator subgroup G'' of the link group G if and only if the $ \mu $th Alexander ideal $ {\mathcal{E}_\mu }(L)$ is principal, generalizing the result announced for $ \mu = 2$ by R. H. Crowell and E. H. Brown. These two properties were separately hypothesized as characterizations of boundary links by R. H. Fox and N. F. Smythe.

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Keywords: Homology boundary link, longitude, Seifert surface, maximal abelian covering, Mayer-Vietoris sequence, second commutator subgroup, Alexander ideal, annihilator, principal ideal
Article copyright: © Copyright 1978 American Mathematical Society

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