On the space of morphisms between étale groupoids
Abstract
Description
Given two étale groupoids $\Cal G$ and $\Cal G'$, we consider the set of pointed morphisms from $\Cal G$ to $\Cal G'$. Under suitable hypothesis we introduce on this set a structure of Banach manifold which can be considered as the space of objects of an étale groupoid whose space of orbits is the space of morphisms from $\Cal G$ to $\Cal G'$.
Amstex, 12 pages. In this revised version, we correct paragraph IV.4, add references and more details on the proofs
Amstex, 12 pages. In this revised version, we correct paragraph IV.4, add references and more details on the proofs