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 Zhurnal SVMO, 2017, Volume 19, Number 4, Pages 33–44 (Mi svmo679)

Mathematics

Foliated models for orbifolds and their applications

N. I. Zhukova

National Research University – Higher School of Economics in Nizhny Novgorod

Abstract: A foliated model is constructed for every orbifold. Such model is a foliation with the leaf space coinciding with the orbifold. The canonical projection onto the leaf space is a submersion in the category of orbifolds. We prove that the group of all diffeomorphisms of an orbifold is isomorphic to the group of basic automorphisms (in the category of foliations) of the constructed model foliation. In terms of the model foliations necessary and sufficient conditions are found for orbifold to be good. As the application we obtain that every orbifold admitting Cartan geometry of zero curvature is good.

Keywords: orbifold, foliation, Ehresmann connection for a foliation, Cartan geometry

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations 17-11-01041

DOI: https://doi.org/10.15507/2079-6900.19.201704.33-44

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UDC: 514
MSC: Primary 53C12; Secondary 54H15, 57R18

Citation: N. I. Zhukova, “Foliated models for orbifolds and their applications”, Zhurnal SVMO, 19:4 (2017), 33–44

Citation in format AMSBIB
\Bibitem{Zhu17} \by N.~I.~Zhukova \paper Foliated models for orbifolds and their applications \jour Zhurnal SVMO \yr 2017 \vol 19 \issue 4 \pages 33--44 \mathnet{http://mi.mathnet.ru/svmo679} \crossref{https://doi.org/10.15507/2079-6900.19.201704.33-44} \elib{https://elibrary.ru/item.asp?id=30775151}