  In this article, we investigate the topological structure of large scale
interacting systems on infinite graphs, by constructing a suitable cohomology
which we call the uniform cohomology. This provides a new perspective for the
identification of macroscopic observables from the microscopic system. As a
straightforward application of our theory when the underlying graph has a free
action of a group, we prove a certain decomposition theorem for shift-invariant
closed uniform forms. This result is a uniform version in a very general
setting of the decomposition result for shift-invariant closed $L^2$-forms
originally proposed by Varadhan, which has repeatedly played a key role in the
proof of the hydrodynamic limits of nongradient large scale interacting
systems. In a subsequent article, we use this result as a key to prove
Varadhan's decomposition theorem for a general class of large scale interacting
systems.
