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Transactions of the American Mathematical Society

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

 

 

Homology invariants of cyclic coverings with application to links


Authors: Y. Shinohara and D. W. Sumners
Journal: Trans. Amer. Math. Soc. 163 (1972), 101-121
MSC: Primary 55.20
DOI: https://doi.org/10.1090/S0002-9947-1972-0284999-X
MathSciNet review: 0284999
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Abstract: The main purpose of this paper is to study the homology of cyclic covering spaces of a codimension two link. The integral (rational) homology groups of an infinite cyclic cover of a finite complex can be considered as finitely generated modules over the integral (rational) group ring of the integers. We first describe the properties of the invariants of these modules for certain finite complexes related to the complementary space of links. We apply this result to the homology invariants of the infinite cyclic cover of a higher dimensional link. Further, we show that the homology invariants of the infinite cyclic cover detect geometric splittability of a link. Finally, we study the homology of finite unbranched and branched cyclic covers of a link.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0284999-X
Keywords: Infinite cyclic cover, $ k$-fold unbranched cyclic cover, $ k$-fold branched cyclic cover, integral invariant, rational invariant, linear graph in $ {S^3}$, $ n$-link of multiplicity $ \mu $, geometrically $ k$-splittable link, completely splittable link, nonsplittable link, null-cobordant link, $ q$-simple link
Article copyright: © Copyright 1972 American Mathematical Society