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Apr 10, 2015 at 8:25 comment added ThiKu So your point is that $\pi^*$ is injective, which follows from existence of an averaging homomorphism on rational cochains, left-inverse to $\pi^*$.
Apr 10, 2015 at 6:39 vote accept Shiquan Ren
Apr 10, 2015 at 4:07 history answered abx CC BY-SA 3.0