Let $\pi\colon P\to M$ be a principal bundle and $p$ an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define an homology map $\chi^{ k} : H_{ 2r-k-1}(M)\times H_{ k}(\mathcal{ F}/\mathcal{ G})\to \mathbb{ R}/\mathbb{ Z}$, for $k<r-1$, where $\mathcal{ F} /\mathcal{ G}$ is the moduli space of flat connections of $\pi$ under the action of a subgroup $\mathcal{ G}$ of the gauge group. The differential characters of first order are related to the Dijkgraaf-Witten action for Chern-Simons Theory. The second order characters are interpreted geometrically as the holonomy of a connection in a line bundle over $\mathcal{ F}/\mathcal{ G})$. The relationship with other constructions in the literature is also analyzed.
Categories: math.DG