Hostname: page-component-7f64f4797f-pmsz9 Total loading time: 0 Render date: 2025-11-03T06:36:41.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Mod Odd Modular Coinvariants, Homology Operations, and Limit Spaces

Published online by Cambridge University Press:  20 November 2018

Nondas E. Kechagias
Nondas E. Kechagias*
Affiliation:
Department of Mathematics, University of Crete, Iraklion, Crete, Greece
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 compute the homology of limn->∞ (Gn ≀ X), where (Gn ) is a system of subgroups of Σpn containing a p-Sylow subgroup (Σpn p) and satisfying certain properties. We show that H*(limn->∞(Gn, ≀ X);Z/pZ) is built naturally over homology operations related to (Gn ). We describe this family of operations using modular coinvariants.

Keywords

55S55N18Ghomology operationsDyer-Lashof algebramodular coin variants

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 803 - 819
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Campbell, H. E. A. and McCleary, J., Homology operations and invariant theory, in preparation.Google Scholar
2. Campbell, H. E. A., Kechagias, N. E. and McCleary, J., Homology operations and parabolic subgroups for p — 2, in preparation.Google Scholar
3. Cartan, H. and Eilenberg, S., Homological Algebra, Princeton University Press, 1956.Google Scholar
4. Cohen, F., Lada, T. and May, P. J., The homology of iterated loop spaces, Lecture notes in Mathematics 533(1975).Google Scholar
5. Dyer, E. and Lashof, R. K., Homology of iterated loop spaces, American Journal of Mathematics 84( 1962), 35–88.Google Scholar
6. Huynh, Mui, Modular invariant theory and the cohomology algebras of the symmetric group, J. Fac. Sci., Univ. Tokyo 22(1975) 319–369.Google Scholar
7. Huynh, Mui, Homology operations derived from modular coinvariants, Lecture Notes in Mathematics 172 (1985), 85–115.Google Scholar
8. Kechagias, N. E., Ph. D. Thesis, Queen's University, Kingston, Ontario, 1990.Google Scholar
9. Kechagias, N. E., Extended Dyer-Lashof algebras and modular coinvariants, in preparation.Google Scholar
10. Kuhn, N., Chevalley group theory and the transfer in the homology of symmetric groups, Topology 21, 247–264.Google Scholar
11. Madsen, I., On the action of Dyer-Lashof algebra in //*(#), Pacific Journal of Mathematics 60(1975), 235–275.Google Scholar
12. Madsen, I. and Milgram, R. J., The classifying spaces for surgery and cobordism of manifolds, Princeton University Press 92(1979).Google Scholar
13. May, P. J., A general algebraic approach to Steenrod operations, Lecture notes in Mathematics 168(1970), 153–231.Google Scholar
14. Nakaoka, M., Decomposition theorem for homology groups of symmetric groups, Annals of Mathematics 71(1960), 16–42.Google Scholar
15. Nakaoka, M., Homology of the infinite symmetric group, Annals of Mathematics 73(1961), 229–257.Google Scholar
16. Steenrod, N. and Epstein, D. B. A., Cohomology Operations, Princeton University Press 50(1962).Google Scholar