Branched Coverings Defined by Triangulations

A canonical branched covering over each sufficiently good simplicial complex is constructed. Its structure depends on the combinatorial type of the complex. In this way, each closed orientable 3-manifold arises as a branched covering over S3 from some triangulation of S3. This result is related to a theorem of Hilden [9] and Montesinos [16]. The branched coverings introduced admit a rich theory in which the group of projectivities, defined in [11], plays a central role.