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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 119, Issue 1
  • January 1996, pp. 119-137

Unstable homotopy classification of

  • John Martino (a1) and Stewart Priddy (a2)
  • DOI: http://dx.doi.org/10.1017/S030500410007403X
  • Published online: 24 October 2008
Abstract

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.

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[GK]A. Bousfield and D. Kan Homotopy limit, completions and localizations, Lecture Notes in Math. 304 (Springer-Verlag, 1972)

[DZ]W. Dwyer and A. Zabrodsky . Maps between classifying spaces. Lectures Notes in Math. 1298 (Springer-Verlag, 1987) pp. 106119.

[H]B. Huppert . Endliche Gruppen I. (Springer-Verlag, 1967).

[J]S. Jackowski . Group homomorphisms inducing isomorphisms of cohomology. Topology 17 (1978), 303307.

[JMO]S. Jackowski , J. McClure and B. Oliver . Homotopy classification of self-maps of BG via G-actions. Annals of Math. 135 (1992), 183224.

[Ma]U. Martin . Almost all p-groups have automorphism groups a p-group. Bull. Amer. Math. Soc. 15 (1986), 7882.

[MP1]J. Martino and S. Priddy . Classification of BG for groups with dihedral or quaternion Sylow 2-subgroups. J. of Pure and Applied Algebra 73 (1991), 165179.

[MP2]J. Martino and S. Priddy . A classification of the stable type of BG. Bull. Amer.Math. Soc. 27 (1992), 165170.

[Ms]G. Mislin . On group homomorphisms inducing mod-p cohomology isomorphisms. Comment. Math. Helv. 65 (1990), 454461.

[No]D. Notbohm . Maps between classifying spaces. Math. Zeit. 207 (1991), 153168.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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