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 the 3-sphere from some triangulation of S^3. This result is related to a theorem of Hilden and Montesinos. The branched coverings introduced admit a rich theory in which the group of projectivities plays a central role.