# Characterization of branched covers with simplicial branch sets

@article{Luisto2018CharacterizationOB, title={Characterization of branched covers with simplicial branch sets}, author={Rami Luisto and Eden Prywes}, journal={arXiv: Complex Variables}, year={2018} }

The image of the branch set of a PL branched cover between PL $n$-manifolds is a simplicial $(n-2)$-complex. We demonstrate that the reverse implication also holds; i.e., for a branched cover $f \colon \mathbb{S}^n \to \mathbb{S}^n$ with the image of the branch set contained in a simplicial $(n-2)$-complex the mapping can be reparametrized as a PL mapping. This extends a result by Martio and Srebro [MS79].

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