Stoïlow's theorem revisited
Abstract
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.
Main Authors
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202009145850Use this for linking
Review status
Peer reviewed
ISSN
0723-0869
DOI
https://doi.org/10.1016/j.exmath.2019.04.002
Language
English
Published in
Expositiones Mathematicae
Citation
- 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
License
Funder(s)
European Commission
Research Council of Finland
Funding program(s)
ERC Starting Grant
Academy Research Fellow, AoF
ERC Starting Grant
Akatemiatutkija, SA
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
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.
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