English

On the space of morphisms between \'etale groupoids

Geometric Topology 2008-09-18 v2

Abstract

Given two \'etale groupoids \CalG\Cal G and \CalG\Cal G', we consider the set of pointed morphisms from \CalG\Cal G to \CalG\Cal G'. Under suitable hypothesis we introduce on this set a structure of Banach manifold which can be considered as the space of objects of an \'etale groupoid whose space of orbits is the space of morphisms from \CalG\Cal G to \CalG\Cal G'.

Keywords

Cite

@article{arxiv.0707.4673,
  title  = {On the space of morphisms between \'etale groupoids},
  author = {André Haefliger},
  journal= {arXiv preprint arXiv:0707.4673},
  year   = {2008}
}

Comments

Amstex, 12 pages. In this revised version, we correct paragraph IV.4, add references and more details on the proofs

R2 v1 2026-06-21T09:03:35.408Z