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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Algebraic invariants of boundary links

Author: Nobuyuki Sato
Journal: Trans. Amer. Math. Soc. 265 (1981), 359-374
MSC: Primary 57Q45
MathSciNet review: 610954
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Abstract: In this paper we study the homology of the universal abelian cover of the complement of a boundary link of $ n$-spheres in $ {S^{n + 2}}$, as modules over the (free abelian) group of covering transformations. A consequence of our results is a characterization of the polynomial invariants $ {p_{i,q}}$ of boundary links for $ 1 \leqslant q \leqslant [n/2]$. Along the way we address the following algebraic problem: given a homomorphism of commutative rings $ f:R \to S$ and a chain complex $ {C_ \ast }$ over $ R$, determine when the complex $ S{ \otimes _R}{C_ \ast }$ is acyclic. The present work is a step toward the characterization of link modules in general.

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Keywords: Link, boundary link, universal abelian cover, module of type $ L$
Article copyright: © Copyright 1981 American Mathematical Society