Unstable splittings of classifying spaces of P-compact groups

Abstract

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 enjoys most properties of compact Lie groups establishes a program for the classification of these objects. Following the classification of compact connected 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 p–compact group splits into a product if the normalizer of the maximal torus does.