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Hi, let p : E--->B be a covering map. Then we have a result that for every subgroup of ## \pi_1(B) ## we have an associated covering map. Now, going in sort-of the reverse direction, is there a way of figuring out what ## \pi_1(B) ## is, if we know a collection of covering maps for B; what information do we need for these to be able to reconstruct ## \pi_1 (B) ## up to isomorphism?

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