Re: Schreier theory

[jim stasheff <jds@math.upenn.edu>]

Ronald Brown wrote:

>
> There is an interesting account  of extensions of principal bundles and
> transitive Lie groupoids by Androulidakis, developing work of Mackenzie,
> at math.DG/0402007 (not using crossed complexes).
>
> Ronnie Brown
> www.bangor.ac.uk/r.brown
>
> Ronnie Brown
>
This brings to mind an interesting (but insufficiently well known)
treatment by I htink) Dennis Johnson of  extensions
A \to E \to G
of topological groups which are also principal bundles

the classification of such extensions fits into an exact sequence

X --> Y  --> Z
where Z classifies the bundle - forgetting the group structure
and  X is the appropriate H^2 classifying split topolgocical
group extensions i.e. A x G as bundles

jim

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