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I'm trying to classify all 3-fold covering for the fundamental group $G=\langle a,b: abab^{-1}\rangle$. By using fiber action, we can make this by choosing a and act on the set with 3 elements but I'm confused how should I find the deck transformation for every cover? For example when I choose $a=(1)$ act trivially on the set $\{1,2,3\}$, what's deck transformation in this case?

Thanks,

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To produce aprostrophes here (and everywhere, in fact!) you need to type ' and not `: the latter means something else here, as explained on math.stackexchange.com/editing-help –  Mariano Suárez-Alvarez May 9 '12 at 0:16
    
You need to describe the action of $a$ and of $b$ to describe a covering. –  Mariano Suárez-Alvarez May 9 '12 at 0:18
    
I know how to describe the action, but how can I find deck transformation from this action? –  Danny May 9 '12 at 0:48

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