THE QUANTUM CONTENT OF THE NORMAL SURFACES IN A THREE-MANIFOLD

CHARLES FROHMAN, JOANNA KANIA-BARTOSZYNSKA
2008 Journal of knot theory and its ramifications  
The formula for the Turaev-Viro invariant of a 3-manifold depends on a complex parameter t. When t is not a root of unity, the formula becomes an infinite sum. This paper analyzes convergence of this sum when t does not lie on the unit circle, in the presence of an efficient triangulation of the three-manifold. The terms of the sum can be indexed by surfaces lying in the three-manifold. The contribution of a surface is largest when the surface is normal and when its genus is the lowest. 1991
more » ... hematics Subject Classification. 57M27. Key words and phrases. Turaev-Viro invariants of 3-manifolds, normal surface, regular spine, quantum 6j-symbol.
doi:10.1142/s021821650800649x fatcat:4jeegym2yjhddafzvnjis4varm