Calculus of Variations and Geometric Measure Theory

R. Luisto - E. Prywes

Characterization of branched covers with simplicial branch sets

created by luisto on 20 Dec 2018



Inserted: 20 dec 2018
Last Updated: 20 dec 2018

Year: 2018

ArXiv: 1809.10874 PDF


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.

Tags: GeoMeG