  The problem of constructing a quantum theory of gravity has been tackled with
very different strategies, most of which relying on the interplay between ideas
from physics and from advanced mathematics. On the mathematical side, a central
role is played by combinatorial topology, often used to recover the space-time
manifold from the other structures involved. An extremely attractive
possibility is that of encoding all possible space-times as specific Feynman
diagrams of a suitable field theory. In this work we analyze how exactly one
can associate combinatorial 4-manifolds to the Feynman diagrams of certain
tensor theories.
