  The characteristic forms in the bundle of connections of a principal bundle P
over M determine the characteristic classes of P for degree less or equal to
the dimension of M, and differential forms on the space of connections for
higher degree. The equivariant characteristic classes provide canonical
equivariant extensions of this forms, and so cohomology classes in the quotient
space of connections modulo gauge transformations. More generally, given a
closed differential form in M and a characteristic form, we obtain a cohomology
class in the space of connections modulo gauge transformations, and we show
that these classes coincide with some classes previously defined by Atiyah and
Singer.
