Branched Coverings, Triangulations, and 3-Manifolds

2001/08/29 by Ivan Izmestiev, Izmestiev, Ivan, Michael Joswig +1 · 1 citation
Mathematics · #05C10) #05C15 #57M12 (57M25 #57Q99 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:05C15 #msc:57M12 #msc:57Q99

paper · pdf · doi:10.48550/arxiv.math/0108202

v2: several changes to the text body; minor corrections

arxiv created 2002/03/20 · arxiv updated 2009/11/30

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 S³. 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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