We construct Chern–Simons bundles as
–equivariant
–bundles with connection
over the space of connections
on a principal
–bundle
. We
show that the Chern–Simons bundles are determined up to isomorphisms by
their equivariant holonomy. The space of equivariant holonomies is shown to
coincide with the space of equivariant differential characters of order
.
Furthermore, we prove that the Chern–Simons theory provides, in a
natural way, an equivariant differential character that determines the
Chern–Simons bundles. Our construction can be applied in the case in which
is a compact manifold of even dimension and for arbitrary bundle
and
group
.
We also generalize the results to the case of the action of diffeomorphisms
on the space of Riemannian metrics. In particular, in dimension
we
obtain a Chern–Simons bundle over the Teichmüller space.
Keywords
equivariant differential character, equivariant holonomy,
Chern–Simons bundle, space of connections, space of
Riemannian metrics
