Three Manifolds and Graph Invariants

1991/12/24 by S. Kalyana Rama, Rama, S. Kalyana, Siddhartha Sen +1
Computer Science · Mathematics · Physics and Astronomy · #Computational Geometry and Mesh Generation #Data Management and Algorithms #FOS: Mathematics #FOS: Physical sciences #Graph Theory and Algorithms #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA

paper · pdf · doi:10.48550/arxiv.hep-th/9112071

12 pages, 14 with figures

arxiv created 1991/12/24 · openalex publication_date 1991/12/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 S³ and RP³, 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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