Details:
Title  Ideal Turaev–Viro invariants  Author(s)  Simon A. King  Type  Article in Journal  Abstract  Turaev–Viro invariants are defined via state sum polynomials associated to a special spine or a triangulation of a compact 3manifold. By evaluation of the state sum at any solution of the socalled Biedenharn–Elliott equations, one obtains a homeomorphism invariant of the manifold (“numerical Turaev–Viro invariant”). The Biedenharn–Elliott equations define a polynomial ideal. The key observation of this paper is that the coset of the state sum polynomial with respect to that ideal is a homeomorphism invariant of the manifold (“ideal Turaev–Viro invariant”), stronger than the numerical Turaev–Viro invariants. Using computer algebra, we obtain computational results on several examples of ideal Turaev–Viro invariants, for all closed orientable irreducible manifolds of complexity at most 9.  Keywords  Turaev–Viro invariant, Gröbner basis, Quantum invariant, Special spine  ISSN  01668641 
URL 
http://www.sciencedirect.com/science/article/pii/S0166864106003555 
Language  English  Journal  Topology and its Applications  Volume  154  Number  6  Pages  1141  1156  Year  2007  Edition  0  Translation 
No  Refereed 
No 
