A TQFT of Turaev-Viro type on shaped 3-dimensional triangulations

Feng Luo (Rutgers)

Abstract: A shaped triangulation is a finite triangulation of an oriented pseudo 3-manifold where each tetrahedron is an ideal hyperbolic tetrahedron. To each shaped triangulation, we associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3-2 Pachner moves and invariant with respect to shape gauge transformations generated by total dihedral angles around internal edges. The partition function is constructed using hyperbolic gamma functions. This is a joint work with R. Kashaev and G. Vartanov.