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On the volume conjecture for classical spin networks

2009/04/10 by Abdelmalek Abdesselam, Abdesselam, Abdelmalek
Computer Science · Mathematics · Physics and Astronomy · #13A50 #22E70 #57M15 #57M25 #57N10 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Topology (math.GT) #Graph theory and applications #High Energy Physics - Theory (hep-th) #Topological and Geometric Data Analysis #gr-qc #hep-th #math.CO #math.GT #msc:13A50 #msc:22E70 #msc:57M15 #msc:57M25 #msc:57N10

paper · pdf · doi:10.48550/arxiv.0904.1734

More than 200 diagrams, pdf is better for download. Minor corrections, references added

openalex publication_date 2009/04/10 · arxiv created 2009/05/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an upper bound for the evaluation of all classical SU(2) spin networks conjectured by Garoufalidis and van der Veen. This implies one half of the analogue of the volume conjecture which they proposed for classical spin networks. We are also able to obtain the other half, namely, an exact determination of the spectral radius, for the special class of generalized drum graphs. Our proof uses a version of Feynman diagram calculus which we developed as a tool for the interpretation of the symbolic method of classical invariant theory, in a manner which is rigorous yet true to the spirit of the classical literature.

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