# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 19th 2009
• (edited Dec 19th 2009)

I intend to considerbly expand the story at Atiyah Lie groupoid. But this afternoon I didn't get as far as I intended to, and now I have to quit and visit my parents. So this is to be continued. But so far I did this:

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeDec 21st 2009
• (edited Dec 21st 2009)

in the section Relation to Differential Nonabelian Cohomology at Atiyah Lie groupoid details of the claim and the proof of how the Atyiah Lie groupoid $At(P) \to \Pi(X)$ of a G-principal bundle $P \to X$ is a quotient of the homotopy fiber of the morphism $\Pi(X) \to \mathbf{B}AUT(G)$ induced from a choice of connection on $P$.

I tried to present the argument in a supposedly nicely geometric fashion, with the homotopy pullback computed in terms of 2-groupoid incarnations of universal 2-bundles, but due to the restrictions of MathML diagrams it may look now a bit more awkward than it should, unfortunately.

I'll try to polish this further, eventually.