G-degree for singular manifolds (Q1671970)

The Gurau degree (or G-degree for short) of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. A singular (PL) \(d\)-manifold \((d > 1)\) is a compact connected \(d\)-dimensional polyhedron admitting a simplicial triangulation where the links of vertices are closed connected \((d-1)\)-manifolds, while the links of all \(h\)-simplices with \(h > 0\) are PL \((d - h - 1)\)-spheres. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds.