The Quantum Content of the Normal Surfaces in a Three-Manifold

Details The Quantum Content of the Normal Surfaces in a Three-Manifold The Quantum Content of the Normal Surfaces in a Three-Manifold

2003-10-17

arxiv.org/abs/math/0310273v1

Mathematics

Geometric Topology

27 pages

Scientific paper

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.

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