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Algebraic Invariants of Boundary Links

Nobuyuki Sato
Transactions of the American Mathematical Society
Vol. 265, No. 2 (Jun., 1981), pp. 359-374
DOI: 10.2307/1999739
Stable URL: http://www.jstor.org/stable/1999739
Page Count: 16
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Algebraic Invariants of Boundary Links
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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 Sn+2, as modules over the (free abelian) group of covering transformations. A consequence of our results is a characterization of the polynomial invariants pi,q of boundary links for 1 ⩽ q ⩽ [ n/2 ]. Along the way we address the following algebraic problem: given a homomorphism of commutative rings f: R → S and a chain complex C* over R, determine when the complex S ⊗R C* is acyclic. The present work is a step toward the characterization of link modules in general.

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