Branched coverings

Basic results on combinatorial branched coverings between relative geometric cycles are given. It is shown that every geometricn-cycle is a branched covering overS″. If the downstairs space of a branched covering is locally simply connected then the branched set is a pure subcomplex of codimension 2. Finally, several Hurwitz-like theorems on existence and representation of branched coverings between relative geometric cycles are derived.