  We present the Hamiltonian analysis of the theory of gravity based on a
Lagrangian density containing Hilbert-Palatini term along with three
topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these
topological terms modifies the symplectic structure non-trivially. The
resulting canonical theory develops a dependence on three parameters which are
coefficients of these terms. In the time gauge, we obtain a real SU (2) gauge
theoretic description with a set of seven first class constraints corresponding
to three SU (2) rotations, three spatial diffeomorphism and one to evolution in
a timelike direction. Inverse of the coefficient of Nieh-Yan term, identified
as Barbero-Immirzi parameter, acts as the coupling constant of the gauge
theory.
