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Sep 25, 2017 at 12:17 vote accept ort96
Sep 24, 2017 at 8:41 vote accept ort96
Sep 24, 2017 at 8:51
Sep 22, 2017 at 1:08 comment added Misha @ort96: Yes, you are right, I was thinking about simply-connected $F$. The cover $\tilde{Y}\to Y$ is the one corresponding to the kernel of the natural homomorphism $\pi_1(Y)\to G$, so its fundamental group will be isomorphic to $\pi_1(F)$. The point is that $EG$ is contractible.
Sep 21, 2017 at 18:33 comment added ort96 Thanks! I'll have to read more on classifying spaces to fully understand this. Doesn't $F \cong \widetilde {Y} $ imply $F $ simply connected? So perhaps $\widetilde {Y}$ is not universal?
Sep 20, 2017 at 3:14 history answered Misha CC BY-SA 3.0