Orbifolds as diffeologies

Patrick Iglesias, Yael Karshon, Moshe Zadka

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)2811-2831
Number of pages21
JournalTransactions of the American Mathematical Society
Volume362
Issue number6
DOIs
StatePublished - Jun 2010
Externally publishedYes

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