The existence of universal flat topological connections with discrete structure group

Abstract

In a topological connection theory, we give a general way of constructing flat slicing functions in locally trivial principal bundles with a discrete group as structure group. Slicing functions play a role of connections in smooth category. By applying this construction to the universal principal bundle over a classifying space which comes from the Milnor construction, we obtain an explicit description of the universal flat slicing function. Using this explicit nature, we show that flat slicing functions given to respective contexts are pulled back from the universal one.