2003/10/17 by Charles Frohman, Frohman, Charles, Joanna Kania-Bartoszynska +1
Mathematics · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M27
paper · pdf · doi:10.48550/arxiv.math/0310273
27 pages
arxiv created 2003/10/17 · arxiv updated 2009/12/01
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.