Sto\"ilow's theorem revisited

Rami Luisto; Pekka Pankka

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arXiv · 1701.05726

Sto\"ilow's theorem revisited

Rami Luisto·Pekka Pankka

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Abstract

Sto\"ilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps.

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Rami Luisto, Pekka Pankka. 2017-01-20. Sto\"ilow's theorem revisited. https://arxiv.org/abs/1701.05726

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