Longitudes of a link and principality of an Alexander ideal

Hillman, Jonathan A.

doi:10.1090/S0002-9939-1978-0507341-6

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
DOI: https://doi.org/10.1090/S0002-9939-1978-0507341-6
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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