Differential characters and cohomology of the moduli of flat connections.

Let π:P→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 a homology map χk:H2r-k-1(M)×Hk(F/G)→R/Z, for k<r-1, where F/G is the moduli space of flat connections of π under the action of a subgroup 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 F/G. The relationship with other constructions in the literature is also analyzed. [ABSTRACT FROM AUTHOR]