The problem of constructing a quantum theory of gravity has been tackled withvery different strategies, most of which relying on the interplay between ideasfrom physics and from advanced mathematics. On the mathematical side, a centralrole is played by combinatorial topology, often used to recover the space-timemanifold from the other structures involved. An extremely attractivepossibility is that of encoding all possible space-times as specific Feynmandiagrams of a suitable field theory. In this work we analyze how exactly onecan associate combinatorial 4-manifolds to the Feynman diagrams of certaintensor theories.
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