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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Orbifolds as diffeologies


Authors: Patrick Iglesias, Yael Karshon and Moshe Zadka
Journal: Trans. Amer. Math. Soc. 362 (2010), 2811-2831
MSC (2010): Primary 57R18
Published electronically: January 7, 2010
MathSciNet review: 2592936
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Abstract: We consider orbifolds as diffeological spaces. This gives rise to a natural notion of differentiable maps between orbifolds, making them into a subcategory of diffeology. We prove that the diffeological approach to orbifolds is equivalent to Satake's notion of a V-manifold and to Haefliger's notion of an orbifold. This follows from a lemma: a diffeomorphism (in the diffeological sense) of finite linear quotients lifts to an equivariant diffeomorphism.


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Additional Information

Patrick Iglesias
Affiliation: Laboratory of Analysis, Topology and Probability - CNRS, 13453 Marseille Cedex 13, France – and – Department of Mathematics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
Email: piz@math.huji.ac.il

Yael Karshon
Affiliation: Department of Mathematics, The University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
Email: karshon@math.toronto.edu

Moshe Zadka
Email: moshez@divmod.com

DOI: http://dx.doi.org/10.1090/S0002-9947-10-05006-3
PII: S 0002-9947(10)05006-3
Received by editor(s): August 20, 2007
Published electronically: January 7, 2010
Additional Notes: This research was partially supported by the Israel Science Foundation founded by the Academy of Sciences and Humanities, by the National Center for Scientific Research (CNRS, France), and by the National Science and Engineering Research Council of Canada (NSERC)
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.