2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54189In this paper a topological theory of gravity is studied on a four-manifold using the formalism of Capovilla {\sl et al}. We show that it is fact equivalent to Anselmi and Fre's topological gravity using the topological symmetries. Using this formalism gives us a new way to study topological gravity and the intersection theory of gravitational instantons if the (3+1) decomposition with respect to local coordinates is performed.15 pages, LatexHigh Energy Physics - Theorytext