2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198215A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2ω<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.28 pages, REVTeX, Alberta Thy 14-94General Relativity and Quantum Cosmologytext