Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Unstable homotopy classification of S030500410007403X_inline1

John Martinoa1 and Stewart Priddya2

a1 Department of Mathematics and Statistics, University of Western Michigan, Kalamazoo, MI 49008, USA

a2 Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

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.

(Received May 31 1994)

(Revised October 06 1994)