  The purpose of this article is to define the topological realization of a
simplicial presheaf and to prove (under appropriate conditions) that it is
homotopy-invariant under Illusie weak equivalence. In particular this applies
to the site of schemes over $Spec (\cc)$ with the etale or Zariski topologies.
As an application we show how to calculate the topological realization of a
Deligne-Mumford stack. At the end we speculate on how to extend this to the
case of $n$-topoi.
