GEMs and amplitude bounds in the colored Boulatov model

In this paper, we construct a methodology for separating divergencies due to different topological manifolds dual to Feynman graphs in a colored group field theory. After having introduced the amplitude bounds using propagator cuts, we show how Graph-Encoded Manifold (GEM) techniques can be used in order to factorize divergencies related to different parts of the dual topologies of the Feynman graphs in the general case. We show the potential of the formalism in the case of three-dimensional solid torii in the colored Boulatov model.