Differential characters and cohomology of the moduli of flat Connections

Abstract

Let $\pi :P\to M$ 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.

22 pages

References in corpus (2)

• Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex
• Cohomological invariants of a variation of flat connection

Cited by in corpus (4)

• Quantization of Polysymplectic Manifolds
• Equivariant holonomy of U(1)-bundles
• Invariants of families of flat connections using fiber integration of differential characters
• Chern Simons invariants in $KK$ theory