Open and discrete maps with piecewise linear branch set images are piecewise linear maps
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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Journal of the London Mathematical SocietyDate
2021Copyright
© 2020 Wiley-Blackwell
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.
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https://converis.jyu.fi/converis/portal/detail/Publication/47277678
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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
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’).License
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