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.

v2: several changes to the text body; minor corrections

References in corpus (1)

• Lectures on 0/1-polytopes

Cited by in corpus (7)

• Recent progress on the combinatorial diameter of polytopes and simplicial complexes
• Hirsch polytopes with exponentially long combinatorial segments
• Even triangulations of n-dimensional pseudo-manifolds
• Including topology change in Loop Quantum Gravity with topspin network formalism with application to homogeneous and isotropic cosmology
• Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes
• Constructing Combinatorial 4-Manifolds
• Constructing Simplicial Branched Covers