Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps
Complex Variables
2020-12-09 v3 Geometric Topology
Abstract
The image of the branch set of a PL branched cover between PL -manifolds is a simplicial -complex. We demonstrate that the reverse implication also holds: an open and discrete map with the image of the branch set contained in a simplicial -complex is equivalent up to homeomorphism to a PL branched cover.
Cite
@article{arxiv.1809.10874,
title = {Open and Discrete Maps with Piecewise Linear Branch Set Images are Piecewise Linear Maps},
author = {Rami Luisto and Eden Prywes},
journal= {arXiv preprint arXiv:1809.10874},
year = {2020}
}