Three Manifolds and Graph Invariants

Details Three Manifolds and Graph Invariants Three Manifolds and Graph Invariants

1991-12-24

arxiv.org/abs/hep-th/9112071v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 14 with figures

Scientific paper

We show how the Turaev--Viro invariant can be understood within the framework of Chern--Simons theory with gauge group SU(2). We also describe a new invariant for certain class of graphs by interpreting the triangulation of a manifold as a graph consisiting of crossings and vertices with three lines. We further show, for $S^3$ and $RP^3$, that the Turaev-Viro invariant is the square of the absolute value of their respective partition functions in SU(2) Chern--Simons theory and give a method of evaluating the later in a closed form for lens spaces $L_{p,1}$.

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