Abstract
We construct the q-deformed spinfoam vertex amplitude using Chern-Simons theory on the boundary 3-sphere of the 4-simplex. The rigorous definition involves the construction of Vassiliev-Kontsevich invariant for trivalent knot graph. Under the semiclassical asymptotics, the q-deformed spinfoam amplitude reproduce Regge gravity with cosmological constant at nondegenerate critical configurations.
