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Transactions of the American Mathematical Society

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

 
 

 

Total linking number modules


Author: Oziride Manzoli Neto
Journal: Trans. Amer. Math. Soc. 307 (1988), 503-533
MSC: Primary 57Q45
DOI: https://doi.org/10.1090/S0002-9947-1988-0940215-6
MathSciNet review: 940215
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Abstract: Given a codimension two link $ L$ in a sphere $ {S^k}$ with complement $ X = {S^k} - L$, the total linking number covering of $ L$ is the covering $ \hat X \to X$ associated to the surjection $ {\pi _1}(X) \to Z$ defined by sending the meridians to $ 1$. The homology $ {H_{\ast}}(\hat X)$ define weaker invariants than the homology of the universal abelian covering of $ L$.

The groups $ {H_i}(\hat X)$ are modules over $ Z\left[ {t,\,{t^{ - 1}}} \right]$ and this work gives an algebraic characterization of these modules for $ k \geqslant 4$ except for the pseudo null part of $ {H_1}(\hat X)$.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0940215-6
Article copyright: © Copyright 1988 American Mathematical Society

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