The Smooth Hom-Stack of an Orbifold

  • David Michael RobertsEmail author
  • Raymond F. Vozzo
Part of the MATRIX Book Series book series (MXBS, volume 1)


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).


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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia

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