A TOPOLOGICAL CHERN-WEIL THEORY 5

In an Appendix we indicate how the cobar construction of Adams

[1] is connected to our theory. We define a holonomy map between

certain d.g.a. algebras. Every p.t.f. can be "normalised"; and then any

normalised p.t.f. gives rise to a holonomy map, thanks to the cobar

construction. We prove that the map from normalised p.t.f.'s to holon-

omy maps is bijective. As an example we construct a p.t.f. for the

path-space fibration of a connected, triangulable space.