Sto\"ilow's theorem revisited

  title={Sto\"ilow's theorem revisited},
  author={Rami Luisto and Pekka Pankka},
  journal={arXiv: Complex Variables},
  • Rami Luisto, Pekka Pankka
  • Published 2017
  • Philosophy, Mathematics
  • arXiv: Complex Variables
  • Sto\"ilow's theorem from 1928 states that a continuous, light, and open mapping between surfaces is a discrete map with a discrete branch set. This result implies that such mappings between orientable surfaces are locally modelled by power mappings $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having the readers interested in discrete and open mappings in mind.