Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-18T02:03:52.725Z Has data issue: false hasContentIssue false

On the Generalized Cyclic Eilenberg-Zilber Theorem

Published online by Cambridge University Press:  20 November 2018

M. Khalkhali
Affiliation:
Department of Mathematics University of Western Ontario London, Ontario N6A 5B7, e-mail: masoud@uwo.ca
B. Rangipour
Affiliation:
Department of Mathematics University of Western Ontario London, Ontario N6A 5B7, e-mail: brangipo@uwo.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We use the homological perturbation lemma to give an algebraic proof of the cyclic Eilenberg-Zilber theorem for cylindrical modules.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2004

References

[1] Bauval, A., Théorème d'Eilenberg-Zilber en homologie cyclique entière. (1998), preprint.Google Scholar
[2] Burghelea, D., The cyclic homology of the group rings. Comment.Math. Helv. (3) 60 (1985), 354365.Google Scholar
[3] Connes, A., Cohomologie cyclique et foncteurs Extn. C. R. Acad. Sci. Paris Sér. I Math. (23) 296 (1983), 953958.Google Scholar
[4] Dold, A. and Puppe, D., Homologie nicht-additiver Funktoren. Anwendungen, German, French summary, Ann. Inst. Fourier (Grenoble) 11 (1961), 201312.Google Scholar
[5] Feigin, B. L. and Tsygan, B. L., Additive K-theory. K-theory, arithmetic and geometry, Moscow, 1984–1986, 67–209, Lecture Notes in Math. 1289, Springer, Berlin, 1987.Google Scholar
[6] Getzler, E. and Jones, J. D. S., The cyclic homology of crossed product algebras. J. Reine Angew.Math. 445 (1993), 161174.Google Scholar
[7] Goerss, P. G. and Jardine, J. F., Simplicial homotopy theory. Progress in Math. 174. Birkh¨auser Verlag, Basel, 1999.Google Scholar
[8] Hood, C. E. and Jones, J. D. S., Some algebraic properties of cyclic homology groups. K-theory (4) 1 (1987), 361384.Google Scholar
[9] Kassel, C., Homologie cyclique, caractère de Chern et lemme de perturbation. J. Reine Angew.Math. 408 (1990), 159180.Google Scholar
[10] Kassel, C., Cyclic homology, comodules and mixed complexes. J. Algebra 107 (1987), 195216.Google Scholar
[11] Loday, J. L., Cyclic Homology. Springer-Verlag, 1992.Google Scholar
[12] Lane, S. Mac, Homology. Reprint of the 1975 edition. Classics in Math., Springer-Verlag, Berlin, 1995.Google Scholar
[13] Weibel, C. A., An introduction to homological algebra. Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, Cambridge, 1994.Google Scholar