Open and discrete maps with piecewise linear branch set images are piecewise linear maps
Abstract
The image of the branch set of a piecewise linear (PL)‐branched cover between PL 𝑛n‐manifolds is a simplicial (𝑛−2)(n−2)‐complex. We demonstrate that the reverse implication also holds: an open and discrete map 𝑓:𝕊𝑛→𝕊𝑛f:Sn→Sn with the image of the branch set contained in a simplicial (𝑛−2)(n−2)‐complex is equivalent up to homeomorphism to a PL‐branched cover.
Main Authors
Format
Articles
Research article
Published
2021
Series
Subjects
Publication in research information system
Publisher
Wiley-Blackwell
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202012096981Use this for linking
Review status
Peer reviewed
ISSN
0024-6107
DOI
https://doi.org/10.1112/jlms.12404
Language
English
Published in
Journal of the London Mathematical Society
Citation
- Luisto, R., & Prywes, E. (2021). Open and discrete maps with piecewise linear branch set images are piecewise linear maps. Journal of the London Mathematical Society, 103(3), 1186-1207. https://doi.org/10.1112/jlms.12404
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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
The first author was 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 (ERC Starting Grant 713998 GeoMeG ‘Geometry of Metric Groups’).
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