Cohomological invariants of a variation of flat connections

In this paper, we apply the theory of Chern-Cheeger-Simons to construct canonical invariants associated to a r-simplex whose points parametrize flat connections on a smooth manifold X. These invariants lie in degrees (2p−r−1)-cohomology with C/Z-coefficients, for p>r≥1. In turn, this corresponds to a homomorphism on the higher homology groups of the moduli space of flat connections, and taking values in C/Z-cohomology of the underlying smooth manifold X