A regular homotopy version of the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne problem

2014/05/31 by Nariya Kawazumi, Kawazumi, Nariya · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1406.0056

Abstract

By introducing a refinement of the Goldman-Turaev Lie bialgebra, we interpret the divergence cocycle in the Kashiwara-Vergne problem and the Enomoto-Satoh obstructions for the surjectivity of the Johnson homomorphisms as some part of a regular homotopy version of the Turaev cobracket.

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• Poisson algebras of curves on bordered surfaces and skein quantization
• A tensorial description of the Turaev cobracket on genus 0 compact surfaces

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