Feynman diagrams of generalized matrix models and the associated manifolds in dimension four

The problem of constructing a quantum theory of gravity has been tackled with very different strategies, most of which rely 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 four-manifolds with the Feynman diagrams of certain tensor theories. (C) 2000 American Institute of Physics. [S0022-2488(00)02310-0].