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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0507341-6
PII: S 0002-9939(1978)0507341-6
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