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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) -> B is defined, would someone please give me this definition? Apparently it is "clear" but I fail to see this.

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    $\widetilde{x} \mapsto p(x)$? (Where $\widetilde{x}$ is the class of $x$ in $E/\!\mathrm{Aut}(E)$.)2010-09-17
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    Thank you, I feel ashamed...2010-09-23

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Let's remove this question from the list of unanswered questions by up-voting this community wiki answer stating that Agusti Roig's comment above contains the right answer.

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Let's honor Rasmus' creative handling of the software restrictions by downvoting this self-referential community wiki answer.

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    Funny, for a moment I thought you got this idea from http://mathoverflow.net/questions/39626/is-there-a-general-setting-for-self-reference but apparently that post turned up later.2010-09-22