Stoïlow's theorem revisited
Luisto, R., & Pankka, P. (2020). Stoïlow's theorem revisited. Expositiones Mathematicae, 38(3), 303-318. https://doi.org/10.1016/j.exmath.2019.04.002
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Expositiones MathematicaeDate
2020Copyright
© 2019 Elsevier GmbH. All rights reserved.
Stoïlow’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→zk 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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ElsevierISSN Search the Publication Forum
0723-0869Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/32094174
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Related funder(s)
European Commission; Research Council of FinlandFunding program(s)
ERC Starting Grant; Academy Research Fellow, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about funding
R.L. has been partially supported by a grant of the Finnish Academy of Science and Letters, the Academy of Finland (grant 288501 ‘Geometry of subRiemannian groups’) and by the European Research Council (ERCStarting Grant 713998 GeoMeG ‘Geometry of Metric Groups’). P.P. has been partially supported by the Academy of Finland projects #256228 and #297258.License
Except where otherwise noted, this item's license is described as CC BY-NC-ND 4.0