UNSTABLE SPLITTINGS OF CLASSIFYING SPACES OF P-COMPACT GROUPS
D.Notbohm
Dwyer and Wilkerson gave a definition of a p-compact group , which is a loop
space with certain properties and a good generalisation of the notion of
compact lie groups in terms of classifying spaces and homotopy theory; e.g.
every p-compact group has a maximal torus, a normalizer of the
maximal torus and a Weyl
group. The believe or hope that p-compact groups enjoy most properties of
compact Lie groups
establishes a program for the classification of these objects. Following the
classification of connected compact Lie groups, one step in this
program is to show that
every simply connected p-compact group splits into a product of
simply connected simple p-compact groups.
The proof of this splitting theorem is based on the fact that
every classifying space of a \pcg\ splits into a product if the normalizer
of the maximal torus does.