Abstract
There is a recent proposal for effective gauge theories that does not involve a background metric which makes it attractive for quantum gravity. The basic building blocks are new spaces of effective connections and the coarse graining maps which relate them. One space of effective connections can be coarse grained to another one assigned to a ''more macroscopic situation'' and that hence captures less information about the system. We study the geometry of the spaces of effective connections and the coarse graining maps. They have the structure of a fiber bundle where the macroscopic space of effective connections is the base space, the total space is the space of effective connections with more information about the system, and the projection is the coarse graining map. More over, the fiber bundle turns out to be principal and to have a preferred section.