Abstract
LetM andN be quasi-manifolds possibly with boundary, we call afolded-covering p: N→M to a non-degenerate simplicial map, such thatp: N/p −1(ϖM)→M/ϖM is a branched covering. The purpose of this paper will be to classify the folded coverings of a given quasi-manifold by using the representations of a particular group on permutation groups, similar to the monodromy representations for coverings and in such a way that includes these ones a particular case. We shall apply our result to the theory of orbifolds to obtain a presentation (alternative to the one in [H-Q]) of the fundamental group for an orbifold defined on a quasi-manifold.
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