Orbifolds as diffeologies

Details Orbifolds as diffeologies Orbifolds as diffeologies

2005-01-06

arxiv.org/abs/math/0501093v3

Transactions of the American Mathematical Society 362 (2010), 2811-2831.

Mathematics

Differential Geometry

26 pages, 6 figures. Minor changes.

Scientific paper

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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