%
%
%
%%
%
%
KERNELS OF MAPS BETWEEN CLASSIFYING SPACES
%
by D. NOTBOHM
%
Abstract:
For homomorphisms between groups, one can divide out the kernel to get an
injection. Here, we develop a notion of kernels for maps between classifying spaces of compact Lie groups. We show that the kernel is a normal
subgroup in a modified sense and prove a generalization of a theorem of Quillen,
namely, a map $f\colon BG\lra BH\p$ is injective, iff the induced map in
mod-$p$ cohomology is finite. Moreover, for \cclg s, every map
f:BG ---> BH\p from BG into the completion BH\p of BH factors over a
quotient of $G$ in a modified sense. Moreover, this factorisation is an
injection.