Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-28T13:41:12.519Z Has data issue: false hasContentIssue false

Unstable homotopy classification of

Published online by Cambridge University Press:  24 October 2008

John Martino
Affiliation:
Department of Mathematics and Statistics, University of Western Michigan, Kalamazoo, MI 49008, USA
Stewart Priddy
Affiliation:
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

Extract

For nilpotent spaces p-completion is well behaved and reasonably well understood. By p–completion we mean Bousfield–Kan completion with respect to the field Fp [BK]. For non-nilpotent spaces the completion process often has a chaotic effect, this is true even for small spaces. One knows, however, that the classifying space of a compact Lie group is Fp-good even though it is usually non-nilpotent.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[GK]Bousfield, A. and Kan, D.Homotopy limit, completions and localizations, Lecture Notes in Math. 304 (Springer-Verlag, 1972)CrossRefGoogle Scholar
[DL]Dold, A. and Lashof, R.. Principal quasifibrations and fibre homotopy equivalence of bundles. Ill. Jour. of Math. 3 (1959), 285305.Google Scholar
[DZ]Dwyer, W. and Zabrodsky, A.. Maps between classifying spaces. Lectures Notes in Math. 1298 (Springer-Verlag, 1987) pp. 106119.Google Scholar
[G]Gorenstein, D.. Finite groups, 2nd ed. (Chelsea 1980).Google Scholar
[HK]Hakris, J. and Kuhn, N.. Stable decompositions of classifying spaces of finite Abelian p-groups. Math. Proc. Camb. Phil. Soc. 103 (1988), 427449.Google Scholar
[H]Huppert, B.. Endliche Gruppen I. (Springer-Verlag, 1967).CrossRefGoogle Scholar
[J]Jackowski, S.. Group homomorphisms inducing isomorphisms of cohomology. Topology 17 (1978), 303307.CrossRefGoogle Scholar
[JM]Jackowski, S. and McClure, J.. Homotopy decomposition of classifying spaces via elementary abelian subgroups (to appear).Google Scholar
[JMO]Jackowski, S., McClure, J. and Oliver, B.. Homotopy classification of self-maps of BG via G-actions. Annals of Math. 135 (1992), 183224.CrossRefGoogle Scholar
[L]Lee, H.-S.. Thesis, Northwestern Univ. (1994).Google Scholar
[Ma]Martin, U.. Almost all p-groups have automorphism groups a p-group. Bull. Amer. Math. Soc. 15 (1986), 7882.CrossRefGoogle Scholar
[M]Martino, J.. Classifying spaces and properties of finite groups, to appear, J. of Pure and Applied Algebra.Google Scholar
[MP1]Martino, J. and Priddy, S.. Classification of BG for groups with dihedral or quaternion Sylow 2-subgroups. J. of Pure and Applied Algebra 73 (1991), 165179.CrossRefGoogle Scholar
[MP2]Martino, J. and Priddy, S.. A classification of the stable type of BG. Bull. Amer.Math. Soc. 27 (1992), 165170.CrossRefGoogle Scholar
[MP3]Martino, J. and Priddy, S.. Stable homotopy classification of , to appear, Topology.Google Scholar
[Ms]Mislin, G.. On group homomorphisms inducing mod-p cohomology isomorphisms. Comment. Math. Helv. 65 (1990), 454461.CrossRefGoogle Scholar
[MiP]Mitchell, S. and Priddy, S.. Symmetric product spectra and splittings of classifying spaces, Amer. Jour. of Math. 116 (1984), 219232.CrossRefGoogle Scholar
[N]Nishida, G.. Stable homotopy type of classifying spaces of finite groups. Algebraic and Topological Theories (1985), 391404.Google Scholar
[No]Notbohm, D.. Maps between classifying spaces. Math. Zeit. 207 (1991), 153168.CrossRefGoogle Scholar
[P]Puig, L.. Structure locale dans les groupes finis. Mémoire 47 (Supplément au numero de Septembre), Bulletin de la Société Mathématique de France (1976).Google Scholar
[Q]Quillen, D.. Higher algebraic K-theory: 1. In Algebraic K-theory I, Lecture Notes in Math. 341 (Springer-Verlag, 1973) pp. 85147.Google Scholar