# Cover $~E \to B~$ gives a homeomorphism $~E/Aut(E) \to B~$

Let $$p : E \rightarrow B$$ be a cover s.t. Aut(E) acts transitively on $$p^{-1}(b)$$ for some fix $$b \in B$$. Then $$E/Aut(E)$$ is homeomorphic to $$B$$ where $$Aut(E) \subset Cov(E,E)$$. The problem is that I don't even understand how the map $$~E/Aut(E) \to B~$$ is defined, would someone please give me this definition?

Apparently it is "clear" but I fail to see this.

• $\widetilde{x} \mapsto p(x)$? (Where $\widetilde{x}$ is the class of $x$ in $E/\!\mathrm{Aut}(E)$.) Sep 17, 2010 at 13:20
• Thank you, I feel ashamed...
– Down
Sep 23, 2010 at 15:04