Cohomological invariants of a variation of flat connections (Q905811)

This paper describes a higher version of the Cheeger-Chern-Simons theory of secondary classes associated to flat connections. The author considers families of flat connections in a complex vector bundle \(E\to X\) over a smooth compact base, parametrized by an \(r\)-simplex. He constructs some invariants taking values in \(H^*(X,\mathbb{C}/\mathbb{Z})\) for \(*=2p-r-1\) with \(p>r\geq 1\). These invariants are interpreted as a map on the higher homology groups of the moduli space of flat connections, taking values in \(H^*(X,\mathbb{C}/\mathbb{Z})\).