Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
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:
split off Atiyah Lie algebroid from Atiyah Lie groupoid
created a section Relation to differential nonabelian cohomology at Atiyah Lie groupoid that states a claim on how the Atiyah Lie groupoid fits into the story of nonabelian groupoid cohomology -- I wanted to type the proof, too, but ran out of time. Either someone takes it as an exercise and provides the proof, or I'll do so myself later today (or tomorrow)
created a stub for nonabelian groupoid cohomology. There exists a nice reference on "groupoid Schreier theory" that should go there, but I don't have time for that now
created inner automorphism 2-group to provide some background information needed in the statement of the above claim
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 of a G-principal bundle is a quotient of the homotopy fiber of the morphism induced from a choice of connection on .
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.
1 to 2 of 2