  We study the Hamiltonian formulation of the general first order action of
general relativity compatible with local Lorentz invariance and background
independence. The most general simplectic structure (compatible with
diffeomorphism invariance and local Lorentz transformations) is obtained by
adding to the Holst action the Pontriagin, Euler and Nieh-Yan invariants with
independent coupling constants. We perform a detailed canonical analysis of
this general formulation (in the time gauge) exploring the structure of the
phase space in terms of connection variables. We explain the relationship of
these topological terms, and the effect of large SU(2) gauge transformations in
quantum theories of gravity defined in terms of the Ashtekar-Barbero
connection.
