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Proceedings of the American Mathematical Society

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Alexander modules


Author: Nobuyuki Sato
Journal: Proc. Amer. Math. Soc. 91 (1984), 159-162
MSC: Primary 57Q45; Secondary 18G15
DOI: https://doi.org/10.1090/S0002-9939-1984-0735584-8
MathSciNet review: 735584
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Abstract: The Alexander modules of a link are the homology groups of the universal abelian cover of the complement of the link. For a link of $ n$-spheres in $ {S^{n + 2}}$, we show that, if $ n \geqslant 2$, the Alexander modules $ {A_2}, \ldots ,{A_n}$ and the torsion submodule of $ {A_1}$ are all of type $ L$. This leads to a characterization, below the middle dimension, of the polynomial invariants of the link. These results were previously proven for the special case of boundary links.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735584-8
Keywords: Alexander module, link module
Article copyright: © Copyright 1984 American Mathematical Society

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