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# On the homology of finite abelian coverings of links

Published:1997-09-01
Printed: Sep 1997
• J. A. Hillman
• M. Sakuma
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## Abstract

Let $A$ be a finite abelian group and $M$ be a branched cover of an homology $3$-sphere, branched over a link $L$, with covering group $A$. We show that $H_1(M;Z[1/|A|])$ is determined as a $Z[1/|A|][A]$-module by the Alexander ideals of $L$ and certain ideal class invariants.
 Keywords: Alexander ideal, branched covering, Dedekind domain, knot, link.
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45}