Homology Invariants of Cyclic Coverings with Application to Links

Y. Shinohara, D. W. Sumners
1972 Transactions of the American Mathematical Society  
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
more » ... nfinite 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. Received by the editors December 21, 1970. AMS 1970 subject classifications. Primary 55A10, 55A25, 57C45. Key words and phrases. Infinite cyclic cover, Ar-fold unbranched cyclic cover, A:-fold branched cyclic cover, integral invariant, rational invariant, linear graph in S3, n-link of multiplicity ft, geometrically A:-splittable link, completely splittable link, nonsplittable link, null-cobordant link, ^-simple link.
doi:10.2307/1995710 fatcat:szznd5khsbcybbbdumqce56e4i