The Generating Functional of the Kontsevich Integral and its Derivation as a Holonomy

2012/02/25 by Renaud Gauthier, Gauthier, Renaud · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #Quantum Algebra (math.QA) #math.GT #math.QA

paper · pdf · doi:10.48550/arxiv.1202.5694

46 pages

arxiv created 2012/02/25 · openalex publication_date 2012/02/25 · arxiv updated 2012/02/28 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We introduce an algebra bundle of chord diagrams over the configuration space of N points in the complex plane on which we put the Knizhnik-Zamolodchikov connection. For that particular connection, the holonomy along a loop in the base is shown to be generating the Kontsevich integral for that loop's associated braid.

Citations

• Vassiliev and Quantum Invariants of Braids

Cited by

• A Stringy Generalization of the Kontsevich Integral

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