Branched Coverings, Triangulations, and 3-Manifolds

Details Branched Coverings, Triangulations, and 3-Manifolds Branched Coverings, Triangulations, and 3-Manifolds

2001-08-29

arxiv.org/abs/math/0108202v2

Mathematics

Geometric Topology

v2: several changes to the text body; minor corrections

Scientific paper

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.

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