  With two typical parent actions we have two kinds of dual worlds: i) one of
which contains an electric as well as magnetic current, and ii) the other
contains (generalized) Chern-Simons terms. All these fields are defined on a
curved spacetime of arbitrary (odd) dimensions. A new form of gauge
transformations is introduced and plays an essential role in defining the
interaction with a magnetic monopole or in defining the generalized
Chern-Simons terms.
