Cohomological Invariants of a Variation of Flat Connections

Abstract

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