Branched coverings, triangulations, and 3-manifolds

Abstract

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 S-3 from some triangulation of S-3. This result is related to a theorem of Hilden [11] and Montesinos [16]. The branched coverings introduced admit a rich theory in which the group of projectivities, defined in [13], plays a central role.