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       KERNELS OF MAPS BETWEEN CLASSIFYING SPACES
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                by D. NOTBOHM
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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.