Topological parameters in gravity

We present the Hamiltonian analysis of the theory of gravity based on a Lagrangian density containing the Hilbert-Palatini term along with three topological densities, Nieh-Yan, Pontryagin and Euler. The addition of these topological terms modifies the symplectic structure nontrivially. 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 diffeomorphisms and one to evolution in a timelike direction. The inverse of the coefficient of the Nieh-Yan term, identified as the Barbero-Immirzi parameter, acts as the coupling constant of the gauge theory.