Equivariant characteristic forms on the bundle of connections

The equivariant characteristic forms provide canonical equivariant extensions of these forms, and therefore canonical cohomology classes on A/Gau0P . More generally, for any closed β∈Ωr(M) and f∈IkG , with 2k+r≥dim⁡M , a cohomology class on A/Gau0P is obtained. These classes are shown to coincide with some classes previously defined by Atiyah and Singer.