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arXiv · 1610.05904

The smooth Hom-stack of an orbifold

David Michael Roberts·Raymond F. Vozzo
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Abstract

For a compact manifold M and a differentiable stack \cX presented by a Lie groupoid X, we show the Hom-stack Hom(M,\cX) is presented by a Fr\'echet-Lie groupoid Map(M,X) and so is an infinite-dimensional differentiable stack. We further show that if \cX is an orbifold, presented by a proper \'etale Lie groupoid, then Map(M,X) is proper \'etale and so presents an infinite-dimensional orbifold.

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David Michael Roberts, Raymond F. Vozzo. 2016-10-19. The smooth Hom-stack of an orbifold. https://doi.org/10.1007/978-3-319-72299-3_3

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