Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-17T03:36:17.356Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stable and Unstable Types of Classifying Spaces

Published online by Cambridge University Press:  20 November 2018

Hyang-Sook Lee
Hyang-Sook Lee*
Affiliation:
Department of Mathematics, Ewha Women’s University, Seoul, 120 - 750, Korea, e-mail: hsl@mm.ewha.ac.kr
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.

The main purpose of this paper is to study groups G1, G2 such that H*(BG1, Z/p) is isomorphic to H*(BG2, Z/p) in U, the category of unstable modules over the Steenrod algebra A, but not isomorphic as graded algebras over Z/p.

Keywords

Primary: 55R35secondary: 20J06
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 341 - 351
Copyright
Copyright © Canadian Mathematical Society 1997

References

1. Evens, L., The Cohomology of Groups, Oxford Science Publications, 1991.Google Scholar
2. Henn, H. W., Lannes, J. and Schwartz, L., Analytic functors unstable algebras and cohomology of classifying spaces, Contemporary Math. 96, Amer. Math. Soc. (1989), 197–220.Google Scholar
3. Landrock, P., Finite Group Algebra and Their Modules, London Math. Soc. Lecture Note Series, Cambridge Univ. Press, Cambridge, 1983.Google Scholar
4. Martino, J. and Priddy, S., A classification of the stable type of BG, Bull. Amer.Math. Soc. (1) 27 (1992), 165–170.Google Scholar
5. Martino, J. and Priddy, S., The complete stable splitting of the classifying space of a finite group, Topology 31 (1992), 143–156.Google Scholar
6. Nishida, G., Stable homotopy type of classifying spaces of finite groups, Algebraic and Topological Theories (1985), 391–404.Google Scholar
7. Priddy, S., Recent progress in stable splittings, Homotopy Theory, Proc. of Durham Symposium 1985, London Math. Soc. Lecture Note Series 117 (1987), 149–174.Google Scholar
8. Serre, J. P., Linear Representations of Finite Groups, Springer Verlag, New York, 1977.Google Scholar
9. Steenrod, N. and Epstein, D. B. A., Cohomology Operations, Ann. Math. Studies 50, Princeton Univ. Press, Princeton, 1962.Google Scholar
10. Switzer, R., Algebraic Topology—Homotopy and Homology, Springer Verlag, Berlin, Heidelberg, New York, 1975.Google Scholar