English

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 nn-manifolds is a simplicial (n2)(n-2)-complex. We demonstrate that the reverse implication also holds: an open and discrete map f ⁣:SnSnf \colon \mathbb{S}^n \to \mathbb{S}^n with the image of the branch set contained in a simplicial (n2)(n-2)-complex is equivalent up to homeomorphism to a PL branched cover.

Keywords

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}
}