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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Orbifolds as diffeologies
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by Patrick Iglesias, Yael Karshon and Moshe Zadka PDF
Trans. Amer. Math. Soc. 362 (2010), 2811-2831 Request permission

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
  • MR Author ID: 213548
  • 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
  • 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)
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 2811-2831
  • MSC (2010): Primary 57R18
  • DOI: https://doi.org/10.1090/S0002-9947-10-05006-3
  • MathSciNet review: 2592936