The Smooth Hom-Stack of an Orbifold
For a compact manifold M and a differentiable stack Open image in new window presented by a Lie groupoid X, we show the Hom-stack Open image in new window is presented by a Fréchet–Lie groupoid Map(M, X) and so is an infinite-dimensional differentiable stack. We further show that if Open image in new window 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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This research was supported under the Australian Research Council’s Discovery Projects funding scheme (project numbers DP120100106 and DP130102578).
- 6.Noohi, B.: Mapping stacks of topological stacks. J. Reine Angew. Math. 646, 117–133 (2010). arXiv:0809.2373
- 7.Roberts, D.M.: Internal categories, anafunctors and localisation. Theory Appl. Categ. 26(29), 788–829 (2012). arXiv:1101.2363
- 8.Roberts, D.M., Vozzo, R.F.: Smooth loop stacks of differentiable stacks and gerbes (2016). Preprint. arXiv:1602.07973
- 9.Stacey, A.: Yet more smooth mapping spaces and their smoothly local properties (2013). Preprint. arXiv:1301.5493
- 10.Weinmann, T.: Orbifolds in the framework of Lie groupoids. Ph.D. thesis, ETH Zürich (2007). https://doi.org/10.3929/ethz-a-005540169