Let (E,[,],φ) be a Lie fiber bundle (defined in last messages). I define a differential over the exterior forms Λ∗(E):
df(s)=φ(s)(f)
dα(s,s′)=φ(s).α(s′)−φ(s′).α(s)−α([s,s′])
for α∈Λ1(E), and f a smooth function. We then have:
d2=0
If φ([s,s′])=[φ(s),φ(s′)].
The Lie cohomology is the cohomology of the so defined complex H∗L(E,R).
Can we define invariants of the Lie fiber bundle?