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On the Homology of Finite Abelian Coverings of Links

Published online by Cambridge University Press:  20 November 2018

J. A. Hillman  and
M. Sakuma
J. A. Hillman
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales 2006, Australia
M. Sakuma
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan
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Abstract

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Let A be a finite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H1(M; Z[1/|A|]) is determined as a Z[1/|A|][A]-module by the Alexander ideals of L and certain ideal class invariants.

Keywords

57M25Alexander idealbranched coveringDedekind domainknotlink
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 309 - 315
Copyright
Copyright © Canadian Mathematical Society 1997

References

[Br] Bredon, G., Introduction to Compact Transformation Groups, Academic Press, New York, London, 1972.Google Scholar
[Da] Davis, J. F., The homology of cyclic branched covers, Math. Ann. 301 (1995), 507–518.Google Scholar
[Fo] Fox, R. H., Free differential calculus, III, Ann. Math. 59 (1954), 195–210.Google Scholar
[Hi] Hillman, J. A., Alexander Ideals of Links, Lecture Notes in Math. 895, Springer-Verlag, Berlin, Heidelberg, New York, 1981.Google Scholar
[HK] Hosokawa, F. and Kinoshita, S., On the homology group of branched cyclic covering spaces of links, Osaka J. Math. 12 (1960), 331–355.Google Scholar
[MM] Mayberry, J. P. and Murasugi, K., Torsion-groups of abelian coverings of links, Trans.Amer.Math. Soc. 271 (1982), 143–173.Google Scholar
[Mi] Milnor, J.W., Introduction to Algebraic K-Theory, Ann. of Math. Study 72, Princeton Univ. Press, Princeton, 1971.Google Scholar
[Sa79] Sakuma, M., The homology groups of abelian coverings of links, Math. Seminar Notes (Kobe) 7 (1979), 515–530.Google Scholar
[Sa81] Sakuma, M., On the polynomials of periodic links, Math. Ann 257 (1981), 487–494.Google Scholar
[Sa82] Sakuma, M., On regular coverings of links, Math. Ann. 260 (1982), 303–315.Google Scholar
[Sa95] Sakuma, M., Homology of abelian coverings of links and spatial graphs, Canad. J. Math. 47 (1995), 201–224.Google Scholar
[Se] Serre, J.-P., Corps Locaux, deuxième édition, Actualités scientifiques et industrielles, Hermann, Paris, 1968.Google Scholar
[We] Weber, C., Sur une formule de R.H.Fox concernant l’homologie des revêtements cycliques, L’Ens. Math. 25 (1979), 261–271.Google Scholar