|
Orbifolds as diffeologies
Author(s):
Patrick
Iglesias;
Yael
Karshon;
Moshe
Zadka
Journal:
Trans. Amer. Math. Soc.
362
(2010),
2811-2831.
MSC (2010):
Primary 57R18
Posted:
January 7, 2010
MathSciNet review:
2592936
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- [BX]
- K. Behrend and P. Xu, Differentiable Stacks and Gerbes, arXiv:math/0605694v2.
- [Che]
- K. T. Chen, Iterated path integral, Bull. Amer. Math. Soc. 83 no. 5 (1977), 831-879. MR 0454968 (56:13210)
- [DM]
- P. Deligne and D. Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. No. 36 (1969), 75-109. MR 0262240 (41:6850)
- [H]
- A. Haefliger, Groupoïdes d'holonomie et classifiants, Astérisque 116 (1984), pp. 70-97. MR 755163 (86c:57026a)
- [Igl1]
- P. Iglesias, Fibrés difféologiques et homotopie, Thèse de doctorat.
- [Igl2]
- P. Iglesias-Zemmour, Diffeology (draft), downloadable from <http://math.huji.ac. il/ piz/> .
- [Kz]
- J. L. Koszul, Sur certains groupes de transformations de Lie, Colloque International du Centre National de la Recherche Scientifique 52 (1953), 137-141. MR 0059919 (15:600g)
- [Me]
- D. Metzler, Topological and Smooth Stacks, arXiv:math/0306176v1.
- [Mo]
- I. Moerdijk, Orbifolds as Groupoids: an Introduction, in: Orbifolds in mathematics and physics (Madison, WI, 2001), 205-222, Contemp. Math. 310, Amer. Math. Soc., Providence, 2002.
MR 1950948 (2004c:22003) - [MP]
- I. Moerdijk and D. A. Pronk, Orbifolds, sheaves and groupoids,
 -Theory 12, 3-21, 1997. MR 1466622 (98i:22004) - [P]
- Richard Palais, On the existence of slices for actions of non-compact Lie Groups, Annals of Math. (2) 73 (1961), 295-323. MR 0126506 (23:A3802)
- [S1]
- I. Satake, On a generalization of the notion of manifold, Proceedings of the National Academy of Sciences 42 (1956), 359-363. MR 0079769 (18:144a)
- [S2]
- Ichiro Satake, The Gauss-Bonnet theorem for V-manifolds, Journal of the Mathematical Society of Japan, Vol. 9., No. 4 (1957), 464-492. MR 0095520 (20:2022)
- [Sou1]
- J. M. Souriau, Groupes différentiels, Differential geometrical methods in mathematical physics (Proc. Conf., Aix-en-Provence/Salamanca, 1979), pp. 91-128, Lect. Notes in Math. 836, Springer, Berlin-New York, 1980. MR 607688 (84b:22038)
- [Sou2]
- J. M. Souriau, Groupes différentiels et physique mathématique, South Rhone seminar on geometry, II (Lyon, 1983), pp. 73-119, Travaux en Cours, Hermann, Paris, 1984. MR 753860 (86a:58001)
- [T]
- Susan Tolman, Ph.D. thesis, Harvard University, 1993.
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2010):
57R18
Retrieve articles in all Journals with
MSC (2010):
57R18
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:
10.1090/S0002-9947-10-05006-3
PII:
S 0002-9947(10)05006-3
Received by editor(s):
August 20, 2007
Posted:
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 of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
