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Orbifolds as diffeologies

Patrick Iglesias·Yael Karshon·Moshe Zadka
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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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Patrick Iglesias, Yael Karshon, Moshe Zadka. 2005-01-06. Orbifolds as diffeologies. https://arxiv.org/abs/math/0501093

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