Algebraic invariants of boundary links

Sato, Nobuyuki

doi:10.1090/S0002-9947-1981-0610954-9

Algebraic invariants of boundary links
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Trans. Amer. Math. Soc. 265 (1981), 359-374 Request permission

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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Boundary links

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