The smooth Hom-stack of an orbifold
Differential Geometry
2021-09-24 v3 Category Theory
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.
Cite
@article{arxiv.1610.05904,
title = {The smooth Hom-stack of an orbifold},
author = {David Michael Roberts and Raymond F. Vozzo},
journal= {arXiv preprint arXiv:1610.05904},
year = {2021}
}
Comments
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