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       ON THE FUNCTOR CLASSIFYING SPACES FOR COMPACT LIE GRROUPS
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%                D. Notbohm
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Abstract:
An old idea of Rector suggest to study compact Lie groups from the homotopy
point of view by looking at the associated classifying spaces.
How much information is lost by this procedure ? It turns out that 
two compact connected Lie groups $G$ and $H$ are isomorphic as Lie groups if and only if the associated classifying spaces $BG$ and $BH$ are 
homotopy equivalent. The proof is based on the following fact: The functor
`classifying space' induces a map from group extension of the form
$G >>> H >>> \Gamma$ to fibrations of the form $BG >>> X >>> B\Gamma$
which turns out to be a bijection for $\Gamma$ a finite 
and $G$ a compact connected Lie group.