  The canonical analysis of the (anti-) self-dual action for gravity
supplemented with the (anti-) self-dual Pontrjagin term is carried out. The
effect of the topological term is to add a `magnetic' term to the original
momentum variable associated with the self-dual action leaving the Ashtekar
connection unmodified. In the new variables, the Gauss constraint retains its
form, while both vector and Hamiltonian constraints are modified. This shows,
the contribution of the Euler and Pontrjagin terms is not the same as that
coming from the term associated with the Barbero-Immirzi parameter, and thus
the analogy between the theta-angle in Yang-Mills theory and the
Barbero-Immirzi parameter of gravity is not appropriate.
