Existence of Branched covers $S^{2}\rightarrow S^{2}$ with prescribed branching data

Yingjie Meng; Zhiqiang Wei; Chuankai Zhou

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arXiv · 2411.08336

Existence of Branched covers $S^{2}\rightarrow S^{2}$ with prescribed branching data

Yingjie Meng·Zhiqiang Wei·Chuankai Zhou

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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.

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Yingjie Meng, Zhiqiang Wei, Chuankai Zhou. 2024-11-13. Existence of Branched covers $S^{2}\rightarrow S^{2}$ with prescribed branching data. https://arxiv.org/abs/2411.08336

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