Is there a way to endow with a topology the set of all atlases of a given topological manifold $M$ ?
Which are the properties of this topology with respect to $M$ ? It would be very nice if this topology have paths between atlases which in some way correspond to isotopies between $(M,\Phi)$ and $(M,\Psi)$ where $\Phi$ and $\Psi$ are two atlases on $M$
Thanks.