Thursday, 17 August 2006

dg.differential geometry - Local Triviality of an Associated Bundle

@Scott: I'm going to add this as an answer because it a bit long for a comment: Sorry, but I'm a bit slow and want to be certain that I understand exactly what you're saying: If (p,v)inPtimesrhomathbbCn, then (alphautimesid)(p,v)=(pi(p),gp,v)inUtimesGtimesmathbbCn, for some gpinG, depending on the choice of alphaU. This is not in UtimesmathbbCn as we would want, moreover it's not even well defined. So by alphaUtimesrhoid do you mean the composition
(idtimesm)circ(idtimesrhotimesid)circ(alphaUtimesid),
that maps
(p,v)mapsto(pi(p),rho(gp)v)?

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