Existence of Branched covers $S^{2}\rightarrow S^{2}$ with prescribed branching data
Geometric Topology
2025-04-10 v5
Abstract
Building on techniques from complex analysis and topology, we establish a remarkable property of branched covers and formulate a complete criterion for the existence of specific types of branched covers between 2-spheres. Our results extend and unify previous work by Jiang (2004), Pervova-Petronio (2006), Zhu (2019), and Wei-Wu-Xu (2024). As applications of our criterion, we present several new families of exceptional branching data.
Cite
@article{arxiv.2411.08336,
title = {Existence of Branched covers $S^{2}\rightarrow S^{2}$ with prescribed branching data},
author = {Yingjie Meng and Zhiqiang Wei and Chuankai Zhou},
journal= {arXiv preprint arXiv:2411.08336},
year = {2025}
}
Comments
13 pages. All suggestions are welcome