On the space of morphisms between étale groupoids

Details On the space of morphisms between étale groupoids On the space of morphisms between étale groupoids

2007-07-31

arxiv.org/abs/0707.4673v2

Mathematics

Geometric Topology

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

Scientific paper

Given two \'etale 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 \'etale groupoid whose space of orbits is the space
of morphisms from $\Cal G$ to $\Cal G'$.

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