The smooth Hom-stack of an orbifold

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 Fréchet-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 étale Lie groupoid, then Map(M,X) is proper étale and so presents an infinite-dimensional orbifold.

Added reference; final version. This is a slightly extended version of a research announcement accepted to appear in the proceedings of "Higher Structures:Advances" at the MATRIX institute, published in the 2016 MATRIX Annals (https://www.matrix-inst.org.au/2016-matrix-annals/), 6 pages, comments welcome

References in corpus (2)

• On the space of morphisms between étale groupoids
• Yet More Smooth Mapping Spaces and Their Smoothly Local Properties

Cited by in corpus (3)

• Lie groupoids of mappings taking values in a Lie groupoid
• Extending Whitney's extension theorem: nonlinear function spaces
• The Banach manifold $C^k(M,N)$