Alexander modules

Sato, Nobuyuki

doi:10.1090/S0002-9939-1984-0735584-8

Alexander modules
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by Nobuyuki Sato PDF

Proc. Amer. Math. Soc. 91 (1984), 159-162 Request permission

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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