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The Smooth Hom-Stack of an Orbifold

Part of the MATRIX Book Series book series (MXBS,volume 1)

Abstract

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

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Acknowledgements

This research was supported under the Australian Research Council’s Discovery Projects funding scheme (project numbers DP120100106 and DP130102578).

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Correspondence to David Michael Roberts .

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Roberts, D.M., Vozzo, R.F. (2018). The Smooth Hom-Stack of an Orbifold. In: de Gier, J., Praeger, C., Tao, T. (eds) 2016 MATRIX Annals. MATRIX Book Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-72299-3_3

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