cohomology of flat bundles and Chern-Simons Functioaln

Abstract

A flat bundle with compact connected structure group and its adjoint bundles of Lie groups are shown to satisfy the Leray-Hirsch theorem. This information has been used to construct a cohomology class of the adjoint bundle whose restriction to each fiber is the class of the Maurer-Cartan 3-form. Then we use this result to define an invariant of a gauge transformation which describes its effect on the Chern-Simons functional defined by choosing a reference connection.