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I have the following question: there seem to be several inequivalent definitions of smooth maps between orbifolds, as indicated in Borzellino and Brunsden - The Stratified Structure of Spaces of Smooth Orbifold Mappings.

My question is: given the easiest situation, where $X$ is a smooth manifold and $Y=M/G$ with $M$ a smooth manifold and $G$ a finite group, do all these notions coincide? That is, is it 'unambiguous' what $C^\infty(X,Y)$ is in this situation?

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  • $\begingroup$ Welcome to MathOverflow! Note that, since your username is automatically displayed below your question, it is not usual (and indeed discouraged) to sign your post in the body. I edited accordingly, while tidying up some other minor issues. $\endgroup$
    – LSpice
    Commented Sep 28, 2023 at 3:59

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