The Chern-Simons state for topological invariants

The covariant canonical formalism for the second Chern and Euler topological invariants which depends of a connection valued in the Lie algebra of SO(3,1) is performed. We show that the Chern-Simons state corresponds to an eigenfunction of zero energy for such characteristic classes, in particular, for the Euler class within self-dual (or anti-self-dual) scenario. In addition, to complete our analysis we develop the Hamiltonian analysis for the theories under study, obtaining a best description of the results obtained with the symplectic method.